Yes, as a historical matter, Sparta was hesitant about adopting imperial ambitions (although there were differences of opinion within Sparta), and while they ostensibly fought Athens to "free the Greeks," they were fine selling out a number of Greek cities to Persia in return for money and ships to fight Athens.
But as you point out, the idea here is that Sparta stands in for Greece, just as Athens does under Pericles. So it's not really a problem.
Well, I don't think they're trying to be all that rigorous with the names/abilities. I mean, "Founding Fathers?" It's just something to evoke the civilization broadly (rather than the leader specifically) and help define its playstyle. They decided Greece was going to be a cultural powerhouse, so they got an extra policy slot.