An ineligible POTUS is never supposed to be allowed to “ACT AS PRESIDENT”, according to the 20th Amendment. It can be debated whether he/she actually can BE president, given that the Constitution says that nobody shall be eligible to the Presidency unless the right age, the right residency, and the right citizenship status. But whether or not he/she IS the President, that person if ineligible is not to be allowed to act as President. Congress was supposed to come up with a line of succession for who should act as President if neither the President-elect nor VP-elect were eligible to do so as of January 20th.
IOW, whether Obama WAS President as of Jan 20, 2009 was irrelevant. The 20th Amendment forbids him from being able to ACT as President unless and until he meets the Constitutional qualifications (age, residency, and citizenship). And he has NEVER met those requirements.
This fantasy you cling to is noteworthy — it goes to show just how little, (pause) people understand how our Federal Triumvirate works (Bicameral legislation) + (Quasi-Oligarchical Judicial system) + (non-successionary Monarch) is supposed to work.
When Obama was sworn in, he left the realm of common and statue law and into the realm of conditional immunity with impeachment oversight. The judiciary has no role other than the CJSCOTUS presiding over impeachment hearings.
If it were otherwise, every President from here on out will be mired in judicial proceedings, like if it was a conservative every Liberal coast to coast will be trying to ‘Tom Delay’ him out of office.