I don't think it would be a violation of her oath if Greene said something like, "AOC's actions were unamerican," or even, "AOC's actions are not American."

But even with this context, I think her saying that AOC "is not an American" is a violation of her oath. You might think, "Greene wouldn't understand the difference," but I think that language, as well as her insults, would not be allowed on the floor of congress, so we already have this requirement that they do understand a tiny bit of decorum. Why not expand it to all public statements?

Honestly, I don't think it's healthy to allow our politicians to lie at all. But that would be even harder to police.