Jeter's reputation could not be further from what you are describing. He would very frequently reject autograph requests. Although to his credit when I met him at a book signing as a kid, he was nice.
My former brother-in-law was a big Yankee fan (I hated the Yankees) and worked at a company that was contracted to do work for the team. He was advised not to ask for autographs or take pictures, but he did speak with all the players. With the exception of one rude player (recently added to the team) all the players were cordial. The player who spoke the longest and was friendliest with him was Jeter who joked that if he was the guy who he constantly hears cheering." Of course, that is just one example.
Many Celebs/athletes don't like to sign autographs since people are now selling them online and making $$$ off it and prefer to sign only for charity. However, I've seen examples of celebs not always being the most amicable. I've met a few that were respectful to me, but didn't have the best reputation with dealing with the public. Often it depends on their mood and the nature of the encounter. Having dinner with their family or at an airport might not be the most ideal setting compared to a meet and greet, book signing, or a charity event.