After reading everything I could find on replacing a President that is what I find. The only way I could see that NOT be the case is if someone then sued to have the Obama Ticket deemed not eligible due to having someone who did not meet the requirements and deceived the voters. (There have been cases filed and affirmed based on equal protection of the voters IIRC.)
Nowhere in the Constitution is such a fantasy land proposition.
If the President is deemed unable or ineligible to serve, the Vice President serves.
This is NOT rocket science, it is in fact one of the very few reasons we even have a Vice President.