Donald Trump, remember, doesn't even believe Obama is an American citizen, or legally qualified to be president to begin with. Believing Obama's a terrorist sympathizer isn't a stretch, if you already believe he's a crypto-Muslim plant conspiring to cover up his own illegitimacy.
[0]https://twitter.com/realDonaldTrump/status/74307515450748928...
[1]http://thinkprogress.org/politics/2016/06/15/3788809/donald-...