Right they both indicate worldwide public awareness.Or maybe they were known about in the 1990's as TOS And ENT indicate.^Of course. The idea isn't that the Eugenics Wars stayed a secret forever, just that our own generation wasn't aware of them. Obviously they were known by Kirk's time, so there's no reason they couldn't have been known by Archer's time, over 150 years after the event.
Neither one indicates anything about American public awareness.