Well, perhaps you can explain what section three of the Twentieth amendment means with the phrase “or if the President elect shall have failed to qualify” What on earth could this be talking about?
And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in the case of the death or other constitutional disability of the President.
I think the "qualify" bit in the 20th amendment (which changed the start of term from March 4 to January 20) is simply updating this scenario.
Imagine a situation where the Electoral College has run into a 269-269 tie, and where the House of Representatives is deadlocked and has not yet chosen a President -- but the Senate HAS selected a new Vice President. This section of the 20th amendment serves to make it clear that the Vice President serves as acting President "until a President shall have qualified."
Why else use the wording "until a President shall have qualified? If there's an argument to me made that some sort of documentation needs to be presented, why wouldn't it be worded to say so? Something like "until a President shall have proven to be eligible for the office." There's historical precedent for a Presidential election being decided after multiple ballots in the House; the 12th amendment's language regarding this situation is made obsolete by the 20th's change in the date; this makes sense to me.