I consider myself Greek, as do the Brothers I do know. Just try to tell us otherwise!!!
Not to speak for the ladies, but I would imagine that most think the same way...
We used to have this dispute with some (not all) Divine 9 members (back in the day) about our "Greekness" (or "Greekdom" if you will) and it usually stemmed from a "narrow-minded" view of what Greekdom actually encompasses. Suffice it to say, we won...
In this case, AXiD670, I think you hit the proverbial "nail on the head". The frats and sorors drawing the line between the "191946 fam" and the rest of the campus Greeks are very likely trying to distance themselves from the negative perceptions of Greek life (on their campus).
I think it depends on the "Greek culture" of the campus you were made in...
It's as simple as this. We are a Greek-Lettered Organization, therefore, we are Greek (as much as any other Greek-Lettered Organization).