Well, for one, basketball is the only American grown sport which is truly international in its scope.
Baseball and Ice Hockey, on the other foot, don't have this type of worldwide recognition (sans the Caribbean and some east Asian countries like Japan for baseball) and of course, Canada and some Scandinavian countries for hockey but we won't go there.
As for basketball, every country I'd visited, in various continents, had heard of Larry Bird and the Boston Celtics. And since Barcelona '92, everyone in the globe wanted to beat America at its own sport. Yes... its own sport, as if Massachusetts/USA has a patent on it like the Edison light bulb.