Hillary Clinton never questioned Barack Obama’s citizenship. Some of her supporters did question his citizenship during the divisive 2008 primary, but are were no links from those disaffected supporters to the candidate herself. 

Trump also did not "finish" the issue before today's concession: He's been tweeting for years to insinuate that the long-form birth certificate the president released was a fake. 

As the leading Republican candidate in January of this year, Trump was still stoking suspicion.

“Who knows [if Obama is a natural-born citizen]? Who knows? Who cares right now? We're talking about something else, OK? I'm going to have my own theory on Obama. Someday I'll write a book, I'll do another book that will do successfully,” he said.