Well, I had a few interesting experiences at Disney actually over this! I recall, at least twice, and I believe at the California Grill, the other at another signature, where I ordered a steak, in fact to be precise, what it really was was the Bison filet they had when I went early last year, and before I could get a word edgewise in, upon ordering I was given a long diatribe from the waitress over how it wouldn't be in my best interests to order this filet strip of Bison anyway other than rare and I had better prepare myself, because it will be rare when they serve it otherwise it would be ruined in the cooking process because Bison doesn't have alot of fat at all, even compared to a filet mignon which is pretty lean, relatively, Bison is far, far leaner.
Now, as it turns out, I always order all of my cuts either medium rare or medium, so this wasn't a big deal for me, but I have to say, if I was like one of the patrons such as our OP, I would have felt very uncomfortable at that point, in stating my wishes for wanting a cut well done, as it felt the waitress was ready to go into battle with me over the issue.
While she never said I
couldn't request it cooked more, because she head me off at the pass and never actually gave the expected and polite, "And how would you like that cooked, sir?" question, I was felt like I couldn't tell her anything but what she wanted to hear.
Of course, this could very well have just been a bison sort of story because it is an unusual sort of meat to be cooking. And perhaps it's a moot point because I have a feeling that the kind of people who would be ordering a cut of meat well done would probably never be seen ordering something unusual off the menu like a Bison anyway?
Me, I'm always ordering stuff like wild boar and ostrich and escargot! And if I recall correctly, the bison was very expensive, like $50 so I certainly didn't wanna order it in a way that would ruin it.