Opinion for the court filed by Circuit Judge RANDOLPH.

Seymour Kleiman appeals from the district court’s judgment dismissing, for want of subject matter jurisdiction, his action to compel the Department of Energy (DOE) to amend its records pursuant to the Privacy Act, 5 U.S.C. § 552a. Kleiman v. United States Dep’t of Energy, 742 F.Supp. 697 (D.D.C.1990). We conclude that the Privacy Act cannot be read to afford Kleiman the relief he seeks, and so affirm.

DOE employed Kleiman from some time before September 30, 1982, until January 26, 1990. The parties are in agreement that prior to September 30, 1982, Kleiman held the position of “Program Analyst,” that the position was correctly classified, and that it carried the grade of GS-14. ^[1] DOE eliminated this position effective September 30, 1982, as part of a reduction in force, and re-assigned Kleiman to the position of “Paralegal Specialist,” which carried the grade of GS-11. On December 12, 1982, DOE re-assigned Kleiman to an essentially identical position in a different sub-office of the agency, and then on February 23, 1989, to a different “Paralegal Specialist” position, requiring somewhat different duties within the same office. His file at DOE contains personnel action forms reciting all of these assignments.

The short of Kleiman’s claim is that, from September 30, 1982, until his resignation in 1990, the duties he actually performed for DOE bore no relation to the job descriptions of the positions he officially occupied ^[2] — that though he carried the title “Paralegal Specialist” he did the work of a “Program Analyst.” He alleges that his personnel records are inaccurate because they reflect the title, not the work, and that the inaccuracies have hindered his search for post-governmental employment.

Kleiman brought the alleged inaccuracies to the attention of DOE in January 1989, and apparently requested that his position be reclassified to match his actual assignment. ^[3] Though the record bears no doc[*337] ument reporting the decision, this request must have been denied, for in February of that year Kleiman filed an appeal with the Office of Personnel Management (OPM). OPM announced its intention to perform a position classification review, during which it would have assessed the duties Kleiman actually performed and determined the correct classification for a position comprised of such duties. However, in April of 1989 Kleiman withdrew his appeal, and OPM’s review never occurred. He did not, however, abandon his objective. In June 1989, he filed with DOE a letter requesting that it amend his records pursuant to the Privacy Act. When DOE denied his request, he filed an appeal with OPM. When that was rejected Kleiman instituted this suit, requesting the district court to “order[ ] defendants to amend plaintiffs personnel file to reflect accurately and completely the actual positions to which plaintiff has been assigned,” among other relief. Complaint at 10 (filed Feb. 5, 1990).

Kleiman argues that his personnel file is not “accurate” within the meaning of the Privacy Act. ^[4] But Kleiman’s — or any other — record can be “accurate” (or inaccurate) only in relation to the state of affairs it is meant to describe. The forms in Klei-man’s file describe his assigned position— they state that his job title was “Paralegal Specialist,” and list the duties of that position. Kleiman does not contest that was his job title, nor does he contest the description of what this position entails. The records, then, are accurate: they correctly reflect the position to which Kleiman officially was assigned. And while the work Kleiman actually did may have entitled him to be placed in a different category, carrying a different job description (and grade), such “error” is not the stuff of which Privacy Act suits are made. Contrast Dickson v. OPM, 828 F.2d 32, 34-35 (D.C.Cir.1987). As one court put it, “[t]he Privacy Act allows for amendment of factual or historical errors. It is not, however, a vehicle for amending the judgments of feder[*338] al officials or ... other[s] ... as those judgments are reflected in records maintained by federal agencies.” Rogers v. United States Dep’t of Labor, 607 F.Supp. 697, 699 (N.D.Cal.1985) (emphasis added & citation omitted).

The need to read the Privacy Act without doing violence to the Civil Service Reform Act of 1978, Pub.L. No. 95-454, 92 Stat. 1111 (codified throughout Title 5, U.S.C.) (CSRA), supports our conclusion that the former does not encompass this type of claim. This court has refused to allow “thé exhaustive remedial scheme of the CSRA” to be “impermissibly frustrated,” Carducci v. Regan, 714 F.2d 171, 174 (D.C.Cir.1983), by granting litigants, under the aegis of the Privacy Act or otherwise, district court review of personnel decisions judicially unreviewable under the CSRA. See Hubbard v. United States EPA, 809 F.2d 1, 4-5 (D.C.Cir.1986), aff'd in part on other grounds sub nom. Spagnola v. Mathis, 859 F.2d 223 (D.C.Cir.1988) (en banc); see also Houlihan v. OPM, 909 F.2d 383, 385 (9th Cir.1990); Towers v. Horner, 791 F.2d 1244 (5th Cir.1986). Taken together, Carducci and Barnhart v. Devine, 771 F.2d 1515 (D.C.Cir.1985), make clear that a direct challenge to a position classifi cation, brought for the first time in federal district court, would not be authorized under the CSRA. Barnhart, 771 F.2d at 1524-26; Carducci, 714 F.2d at 174-75. Yet if we were to allow Kleiman to force DOE to amend his records here, we would be authorizing exactly that.

Kleiman protests that “he is not seeking to ... secure judicial review of federal personnel decisions,” Reply Brief at 6 (internal quotations omitted), but only “seek[s] to ensure ... that his records accurately and fairly reflect his actual job responsibilities with the federal government.” Id. at 8. This seems to us a distinction without a difference. First, we are not sure how the agency responding to this sort of Privacy Act request is supposed to ascertain someone’s “actual job responsibilities” other than by looking at the relevant “federal personnel decision[ ]” assigning and classifying that individual’s position, or by replicating the procedures used to make the decision itself. Kleiman’s apparent answer is that such a determination should be made in a de novo review before a district judge. But that was a mechanism Congress did not provide to a federal employee contesting a classification decision — a decision that can immediately affect the employee’s job title, opportunity for transfer, chance for promotion, or income. It would be strange if Congress nevertheless provided that same cumbersome and expensive mechanism to someone concerned with his possibilities for non-governmental employment. Second, were Kleiman successful, the agency either would have to amend his forms to state he actually had been employed as a Program Analyst, or place another document in his file stating that, in the government’s view, the unamended forms were erroneous. Either way, Klei-man would have achieved the same, impermissible result — a collateral attack on the original personnel decision, bypassing the “exhaustive remedial scheme” provided by Congress. Carducci, 714 F.2d at 174. See generally id. at 173-75; Barnhart v. Devine, 771 F.2d at 1521-23, both setting forth the general scheme for administrative and judicial review of federal personnel actions.

Appellant cites Hubbard for the proposition that the Privacy Act gives the district court jurisdiction over a damage suit for “an adverse personnel action,” Brief for Appellant at 18, quoting Hubbard, 809 F.2d at 5. In reviewing the district court’s action there, however, Hubbard merely “assumed] arguendo [that] the ... document was inaccurate,” 809 F.2d at 3, an assumption we obviously cannot make today. Hubbard decided that any hypothetical inaccuracy did not make out a Privacy Act violation because the plaintiff could not show causation. Id. at 4, 5. That “causation analysis ... was influenced by [the need] not to read the Privacy Act so as to bring it into conflict with the CSRA,” and, no doubt, by the fact that Hubbard’s “complaint really allege[d] only a wrongful personnel decision,” id. at 5. In short, we[*339] think nothing in Hubbard can be construed as conflicting with our decision today. ^[5]

All of the foregoing demonstrates that we agree with the district court’s reasoning about the scope of the Privacy Act and its interrelation with the CSRA. We disagree, however, with the district court’s conclusion that it therefore lacked jurisdiction over the action. “[PJlaintiff’s statement of his own cause of action shows that it is based upon [federal] law[],” Louisville & Nashville R.R. v. Mottley, 211 U.S. 149, 152, 29 S.Ct. 42, 43, 53 L.Ed. 126 (1908), such that it is a “civil action arising under the ... laws ... of the United States.” 28 U.S.C. § 1331. Unless “the alleged claim ... clearly appears to be immaterial and made solely for the purpose of obtaining jurisdiction,” or “wholly insubstantial and frivolous,” Bell v. Hood, 327 U.S. 678, 682-83, 66 S.Ct. 773, 776, 90 L.Ed. 939 (1946), plaintiff’s well-pleaded complaint determines whether his suit “arises under” the laws of the United States for jurisdictional purposes. Id. at 681, 66 S.Ct. at 775. The district court therefore should have denied the government’s motion to dismiss to the extent that motion argued lack of subject matter jurisdiction. See C. Wright, The Law of Federal Courts 102 (4th ed. 1983). However, the same motion also requested that the action be dismissed under Fed.R.Civ.P. 12(b)(6) for failure to state a claim on which relief could be granted. Since we hold that the Privacy Act does not afford relief for Kleiman’s claims, and since we may affirm on different grounds the judgment of a lower court “if it is correct as a matter of law,” United States v. Garrett, 720 F.2d 705, 710 (D.C.Cir.1983) (citation omitted), the judgment of the district court is

Affirmed.