It wasn't that barbarians couldn't become like the Greeks, it was that the Greeks didn't actively spread their culture to other peoples. From what I know the Macedonians were this situation: self-hellenised barbarians who were never accepted as Greeks by their southern neighbours. And perhaps owing to the fact that Macedonians knew they weren't Greeks, their attitude towards non-hellenised people was less harsh than the Greeks.Regardless of high brow attitudes, though, they could and they did. The Greek culture spread immensely over the course of the 1st millennium BC and not just purely from Greek colonization. I think the two attitudes have more in common than you think.