I don't remember a single time that I had a player demand a relative amount of money/years than what he signed for 1 day later in free agency. And more times that not he will sign a considerably cheaper contract to play for a much weaker team.
This happens every offseason - but one unforgettable instance was when Andrew McCutchen (who is from Florida) signed with the 58-104 Giants over my 103-59 Braves (who just lost the WS in 7 games). I offered him a fantastic contract, and he immediately got 'angry' and cut negotiations with me. He then proceeded to take his anger 3,000 miles away from home to play for a pitiful Giants team - for less money - and less years.
I love this game to death but please fix free agency!