I love baseball, but it's not much more a game of athleticism than golf is. Which, of course, is why I'd never hold up a baseball player as a great athlete. Being a good athlete helps you with the running and throwing and catching part of baseball, of course, but the most fundamental part of the part of the game is still hitting and pitching, and pure athleticism doesn't really help anybody much with either of those skills.
(Bo Jackson and Jim Thorpe were two of the greatest athletes in American history, for example, but neither of them could really hit much.)