I think hungrypo and Garvin are saying it pretty well. What the drums actually DO in Jazz is usually more than what's required in other music. For example, in contemporary Jazz, the drummer will not just play a continuous, static beat. They are expected to interact with the music as it goes by- they are more than just a 'timekeeper' and therefore must have the ability to do so. In other words, the skill set is usually more highly developed (or should be) and relies on things others have mentioned, listening, improv, sensitivity, touch, soloing, musiciality and so forth.
That being said, I don't know if I believe that idea though, that Jazz players can play anything. I think 9 times out of 10 when a strict Jazz player plays rock, it sounds lame, same for when a strict rock player plays Jazz. A lot of Jazz players have noodle arms and a lot of rock players have tree trunks when it comes to Jazz. Furthermore, I've seen more than a few Jazz 'drummers' who can play the bare minimum of interdependance, can barely swing on the cymbal, can't play either loudly or quietly and are not comping at all because they don't very well. In a rock setting, say, these guys would suck, no question and would have no gigs. In a Jazz setting, they will be hired by vocalists and others who just want to hear a cymbal, swinging or not and are not even AWARE that they can't do much else. In many, backing Jazz gigs, a drummer can get by with only playing a cymbal. This is brilliant if you do it right but horrific if that's your entire bag=).
I think it's mostly the ideal. In other words, the IDEAL Jazz drummer is ABLE to do anything because of his approach and understanding of the drumset, creativity and ability required to play the music he usually plays, namely, Jazz music. And in that case, it would seem that yes, a Jazz drummer would have the ability to play most other things easier, but in practise, I cannot play double bass drums either....
And yeah, Grunter- what Jazz are you listening to?!
G