Absolutely! It didn't happen to me, but I have a co-worker that was the second choice behind me, and he knows it.
What happened was, the hiring manager (now our boss) wanted to hire two people but was only given budget for one. They made me the offer and told Number Two Guy that he was their second choice, and they were going with me because of blah blah blah. Two weeks later, they were given the budget to hire another person, called him back, and he took the job.
So now we are both happily employed, work on the same team and get along fine even though he knows exactly what happened...actually, come to think of it, that may be WHY we get along...