While thats semi true, sometimes its the opposite. I would take a non pure bred before a 100% pure bred. I believe pure bred dogs have alot of problems that come along with that..hip and joint deterioration, heart/stomache issues, skin sensitivity and allergies.
Anyways, I think it depends on the area.. usually pitbulls are the first to go, they are a highly sought after breed here. Alot of pitbull owners however are usually extremely irresponsible and not capable of handling and training a large strong animal.
A tip on finding good owners is list an ad somewhere for a price. 100, 200, 300$ "adoption fee" and then if you get some interested people that are serious just dont charge them for it.