It seems to me that the hub of the issue about who gets the award
revolves around the difference between comedy and humor.  Twain himself
provides an illustration in How to tell a story:

"The humorous story is told gravely; the teller does his best to conceal
the fact that he even dimly suspects that there is anything funny about
it; but the teller of the comic story tells you beforehand that it is
one of the funniest things he has ever heard, then tells it with eager
delight, and is the first person to laugh when he gets through. And
sometimes, if he has had good success, he is so glad and happy that he
will repeat the "nub" of it and glance around from face to face,
collecting applause, and then repeat it again. It is a pathetic thing to
see."