I think the paint horse started out as a different registry and the AQHA appended it's rules to allow paints, but I'm not absolutely sure and I've forgot my PIN and can't access the AQHA web site.
My old stud is registered with Paint Horse Association. He's a red roan.
Actually, years ago, people bred for Quarter Horses and every now and then, they would get what we now refer to as Paints. They hated it and usually killed the foal. Only fairly recently have people decided that paints are a good thing.
I don't know about the AQHA accepting paints. I'm a member of both APHA and AQHA so I can look that up. The paint horse association is sort of a spin-off of the Quarter Horse Association so I really can't imagine that the Quarter Horse association is accepting paints. Maybe they have loosened the rules a little to allow solid paints with paint horse registry so they can be a member of both associations.
I'll have to look that up later, I gotta get my brood ready for school.