The question of presidential birth legitimacy brought up by “birthers” needs to be addressed. Was our 21st President, Chester A. Arthur born in Vermont or Canada as some have claimed? His mother was an American but his father was from Ireland, so would a Canadian birth invalidate Arthur's Presidency? (Arthur was James Garfield's VP and he became president after the Garfield assassination.) Though there was no definitive evidence of Arthur being foreign born, the issue was a significant diversionary talking point of the 1880 election.
Fast forward 132 years, replacing Canada with Kenya, Arthur with Obama, and you have all the fixings for another full course meal of baloney. I enjoy postulating about outlandish things as much as the next conspiracy nut. I also understand that the burden of proof lies with those making a claim. Repeating something doesn't make it so. There may be a fire where there is smoke, or maybe just a smokescreen.