The Court distinguished between executive officers and quasi-legislative or quasi-judicial officers. The Court held that the latter may be removed only with procedures consistent with statutory conditions enacted by Congress, but the former serve at the pleasure of the President and may be removed at his discretion. The Court ruled that the Federal Trade Commission was a quasi-legislative body because it adjudicated cases and promulgated rules. Thus, the President could not fire a member solely for political reasons. Therefore, Humphrey's firing was improper.

Sounds like what the parent was saying, so not flatly incorrect.

Your comment is way too vague to be declaring anything as flat out wrong. At any rate, federal employees have numerous protections from being fired arbitrarily as laid out by the Civil Service Reform Act of 1978, a law passed precisely to limit arbitrary firing of federal employees, especially for politically motivated reasons.