Untrue.
Each Presidential election cycle results in a person being named "President Elect". A President Elect is the person who assumes the office of President, if they qualify that is, for the next Presidential term of office. If someone is the current President, they can still be the President Elect as well.
Meanwhile, most Freepers know that the Constitution is a far better source than Wikipedia.
So you believe that a re-elected incumbent holds two constitutional offices, president AND president-elect and that there is only a two week period between the counting and certification of the votes of the electors at the Joint Session of Congress and taking the Oath of Office on Inauguration Day when it can be determined whether the president-elect has qualified or not. Whew, that’s a tight schedule.
An interesting position you have there.