He can make a polite request to H.R., and hope that they carry out the request. They don't have to respond to him or verify that they have taken action.
If he can prove that he has suffered injury as a result of the error -- for example, if he's able to confirm that he lost a job opportunity because they incorrectly stated that he was fired -- he has a potential defamation claim; but in the absence of any damages, even if a third party learns of the incorrect information, he doesn't have a basis for a defamation lawsuit.

