The Members of Greek Lettered groups are called "Greeks" because of the letters used to identify their org with. Though they are governed by "Panhellenic" associations, they don't actually affiliate themselves with themselves with Greece.
Many Greek Motto's are written in Latin, with roman numerals as well. They host events like Toga parties which are also Rome-based. Toga's weren't worn by the greeks, so that's a major culture clash.
Black Greeks are a different beast. Stepping, for example, is an ever evolving form of old West African dance. The actual "Stepping" part isn't as dominant as it was in the past,
Today, It's being overshadowed by whatever new dance is in style. Others just flex as if they're 90's R&B videos. Much of today's step shows are called Greek-shows now for that very reason. Not that their's anything wrong with that.
We Americans tend to mix everything up as though it's okay. We also get offensive and combative when people are trying to be informative. It's the American way.