I think that there's also inherently a problem with the definition of "Euro" as it has come to mean "International Player" in a lot of cases. But let me just illustrate the difficulties in trying to apply the word "Euro" and see who counts and who does not:
A Euro player largely means a player born in Europe and developed there before coming here as a pro. Where one might differentiate a bit is guys like Nocioni or Manu, born and raised in Argentina but then went to Spain/Italy for around 5 years.
An American born and raised/developed here who spent a year or two abroad obviously isn't a Euro. I mean, if a born and raised Euro came here and played for a couple years before going back, like Sergio Rodriguez, would anyone think he's an American player?
What we don't have in basketball which we do have in soccer is young Americans ages 14-16 signing in Euro academies and being largely developed overseas. Even then, they're considered Americans developing abroad.