I don't know about that either but section three certainly instructs Congress to name a replacement if the President elect "shall have failed to qualify". This means that the burden of proof is on the President elect and on Congress to ensure that he "qualifies". Since, we're talking about the "President elect", this qualification thing has nothing to do with the electoral college tabulation and verification process. That has to have been done and accepted by the Congress BEFORE there is a "legal" President elect. This "qualification" being sought must therefore pertain to whatever else there is to "qualify" for. Only thing left in the Constitution at this stage is the eligibility requirements from Article two.
This section says to Congress that it is responsible for naming a replacement in the event the President elect dies before becoming President or if the President elect fails to qualify. They must know the answer to BOTH of these conditions and are instructed to act accordingly. Did they do their job? Doesn't look like it.
If Obama is not qualified to be president then he would also not be qualified to be president elect, right? So then wouldn't the 12th Amendment, and its provisions for what to do when no candidate receives a majority of the electoral votes cast, be the applicable amendment and not the 20th?