I would counter your argument by saying that as it pertains to this issue, which hospital he was born in is not a "minor factoid". Especially considering that the location of his birth has been disputed and that it may affect his eligibility to be President. A little more looking into the matter reveals to me that the possible basis for the claim that he was born at that particular hospital is a statement by his sister in 2008 claiming such, and nothing else (at least that I can find). Do you find it an unreasonable stretch to suggest that his sister might be incorrect and that further verification would be reasonable?