For me, the decathlete is the worlds greatest athlete. If you put a decathlete on a soccer pitch, he'll do fine. If you put him on a baseball diamond, he'll look like a fool if he's never played the game. (Try playing slow-pitched softball with people from cultures who play cricket.)
The decathlete could play basketball if he didn't have to score and could play several football positions with the barest of practice. (Assuming he played in a league with people of similar size.)
You've made pointless distinction -- skill and physical ability are inseparable components of "athleticism."
On the contrary. They get separated all the time. Hockey has good skaters, good stick-handlers, goons, etc.
So you're basically telling us that it's possible to be a great athlete, and yet have no skills....
You realize that's not even remotely true. You're saying basically that "athletic" is the same as "physical," but we all know that great athletes have to be both physically gifted, and skilled at what they do.