I am having a hard time wrapping my brain around the difference between resigning and being outed as to legitimacy of actions.
You are right in having a problem with an explanation that sets forth a distinction without a difference as it relates to the effect resigning or being forced out of office would have on past actions by a Constitutionally unqualified president. It makes no difference how he leaves office or when he does, all prior actions are ultra vires, that is without authority and all prior acts are null and void. That is a true Consitutional crisis which will cause grevious harm to this country. Anyone who would deliberately put the country through just epic tragedy should be tried for treason.
There is a large time gap and many legal roadblocks between commencement of discovery to prove up the alleged Kenyan BC and actual constitutional removal of the president, if warranted.
My point is that if Obama resigns before any Kenyan BC even begins to be validated in federal court, removal for ineligibility would be averted and his prior legal acts preserved, or at least the bar to successfully contesting prior legal acts would be much higher. I am guessing. I am not a lawyer.