It may be an unpopular opinion here, but the '60 election was indeed probably stolen. Texas and Illinois were the difference.
Richard Nixon gets hammered a lot, but he decided not to contest the election as he did not want to put the nation through it. Pretty noble, in my opinion. The Repubs had pretty good ground to stand on with the shenanigans in Texas and Illinois, and were urging Nixon to contest.
Kennedy was visibly relieved when Nixon told him he would not contest when the two men met in Palm Beach a few days after the election. I suspect JFK knew he got lucky.