There is still a chance that the 12th could apply. If Obama’s votes are disqualified that would leave McCain with an insufficient number of EV which would then throw it to the House. You could be right that the 20th would be operative but it is not clear which would be involved not knowing what the Congress would do at the critical moment.
What Constitutional provision allows Obama's votes to be disqualified? None I'm aware of. The closest scenario we have to go by is the 1872 election where Horace Greeley died after the election but before the Electoral College met. His votes were not disqualified, they were spread among several Democrats including the vice president elect. If Obama is found ineligible before December 15th then it's likely that his electors would vote for Biden, and he would be the winner. He would only need 270 of them. And if that happens then the 12th Amendment becomes irrelvant.