Yeah, my gelding is a big scramble of TB, QH, and Paint (and he's painted color). So he's registered with APHA! He cannot be registered with AQHA or Jockey Club because 1-he's painted and 2-he's cross-bred.
Here's another question: can an APHA Paint be registered in the Pinto Horse Assoc of America? On the PHAA website, it describes "The Breed" by different height requirements, type requirements, and color (tobiano/overo/breeding stock) requirements. So, doesn't that kind of envelop every horse & pony in the world?