First off, who says they don't? We are US-trained, we are AMGs, most of us that have graduated recently took Step 1 and are in ACGME residencies. To be completely honest I don't hear MDs advertise themselves as "US-trained," nor does anyone seem to care. When people come into clinic, I'm their doctor. Its up to them if they want me to be their DO, but most couldn't care less.
Its come up so few times in residency, and most of the time people say something like, "oh my favorite doctor was a DO." You don't notice it, the only times I do is when I bump into another DO.
Maybe it'll be different if I move out West, but I don't think so.