It isn't immediately clear if there is any cause of action against the company; as you note, your father was an at-will employee, and a report of bad driving (even if unverified) would not ordinarily be an unlawful reason to terminate an at-will employee (even if unreasonable from the standpoint of trying to deny him unemployment insurance). If the supervisor made up the report, or lied about something, there may well be a cause of action against the supervisor. He may wish to have his situation reviewed in detail by a plaintiff-side employment lawyer.

