As a practical matter it takes you a good 10 generations to have anyone in your line eligible for the Society of Cincinatti. The biggy is one of the two 16th century societies ~
BTW, those Italian and Greek guys didn't, for the most part, run off with native born women ~ they went back home to find women. That's why you can't use the 1 out of 7 or 1 out of 10 thing as a universal condition ~ quite common for first generation people to stick together
And the 14th says explicitly all born here are equal. For a reason too, pairs up with the 13th.