Your understanding is correct, but people who dislike aces really love to pretend that only one of our identities matter, and they pick and choose which one in whatever way lets them pretend that their biases are real.
Ace and aro are non-straight identities, even if some heteroromantic aces might ID as straight. Any attempt to force such an identity on all of them is aphobia, pure and simple.
-Dew
