My pocket copy of The Constitution says otherwise.
What's your read on it? As I see it the electors can vote for anyone they want, if BHO is discovered to be ineligible they would probably rally around Biden or HRC. If nobody gets 270 votes the decision falls to the House, which again would result in either President Biden or Clinton being sworn in.
If Obama is sworn in and later found to be ineligible, if he doesn't resign, he would have to be impeached by the House and removed from office by the Senate. (Not holding my breath. I suspect I know how senators McCain, Graham & Franken would vote.) If they did remove him from office, Biden becomes President.
Your interpretation may not be correct.