Right. A skeleton doesn't "know" anything about a mesh. It just moves based on an animation that has been authored for it. A mesh is skinned, or weighted to a skeleton, and "knows" nothing about a given animation just that the skeleton it is skinned to tells it to move or twist or deform.
Because of this. Many online games, for performance reasons only have a single biped skeleton for all characters and NPCs.
But that doesn't mean you couldn't have a single mesh work on 20 different skeletons. There traditionally just haven't been any reasons to.