Too late for playing the misquote card, he has been on every show imaginable repeating that he answered truthfully but refuses to go into further detail. I'm not sure what their strategy is on this one, it's been a strange turn of events.
Look, they could offer him a job without saying explicitly "you get this job if you drop out of the race". By taking the job he would have to drop out of the race and problem solved. He just let the cat out of the bag that they tried this move on him.
obviously it would be understood that they were offering him this job to get him out of the race. if there is proof of the offer someone's head is going to roll. book it.
he damn sure won't be implicating the WH.