Scott Thompson was recently fired as CEO of Yahoo after four months on the job. He had asserted he had two degrees; one in accounting and another in computer science. His degree was actually in accounting only.
Elizabeth Warren, the Oklahoma Senate candidate and Harvard professor who cites "family lore" that she is 1/32nd Cherokee, and used that "fact" to claim minority status. Harvard Law School and the University of Pennsylvania listed her as a minority faculty member when she taught there. It would appear she is not any part Cherokee.
Now as I said, I encourage embellishment if you actually have something to embellish. In the two cases above they simply lied and you should never lie on your resume and even more so, never lie on an employment application.
When I first started in accounting in the 1970's, companies took your word you had a college degree. About 1978 I was working for NCR Corporation in Millsboro and the company decided those who said they college degrees should produce them or have their college transcription sent to the personnel department. The head of the purchasing department who had said he had a master degree and a couple of other degrees decided to seek employment elsewhere within a week of that announcement.
Always make sure there is that grain of truth in anything you put down on a resume or employment application.