Poor Gerald Ford

In the Section Three litigation, one argument for why the President and Vice-President are not officers of the United States is that only appointed federal officials are officers of the United States. If correct, it's a bright and clean dividing line, right?

But what about Gerald Ford? He was an appointed Vice-President and President. And what about Nelson Rockefeller, who was also an appointed Vice-President. Were they officers of the United States? If not, why not? (I can't find anyone who addressed this in the 1970s.)

It's fair enough to say that the Twenty-Fifth Amendment just creates an exception to the appointed/elected distinction for officers of the United States (if Ford and Rockefeller were such officers). But if the 25th Amendment could make such an exception to this purported rule, why not the 14th Amendment?