I don't recall the Cheers episode in question, but I've watched Jeopardy lots of times, and with the way the questions are written and special instructions are given for the categories when necessary, multiple correct answers are hardly ever possible.
I do --except that his question wasn't really consistent with the Jeopardy category.
I think they were details that should be included, simply because the word play trick question is very common in these games. However, further explanation of details is also a common point of them, so there's no point in getting bitter.
Redefining the rules may be common, but it's hardly fair or unfrustrating, and it offends Occam's razor.
Now, if it's one of those "give a statement and then let the person ask questions until they figure out the whole story" kinds of things (like the lady who jumped out of the hot air balloon earlier in the the threads), that's different--but I assumed you were posing an actual riddle, not one of those things.