That's the reason in a nutshell but there is lots more to it. In the early 1960's there were two paint horse associations, the American Paint Stock Horse Association and the American Paint Quarter Horse Association. They merged to form the American Paint Horse Association.
Lots of interesting reading, if you like paints, in the books "The American Paint Horse" by Glynn W. Haynes and the book that the paint horse association puts out called "The American Paint Horse, A Photographic Portrayal".
The quick, condensed, short, sweet, I don't have much break time reason. :)