Not correct when it comes to Arabians. The AHA doesn't allow a horse to be classified as a purebred if there's even a drop of 'other' blood in the animal. That rule was started about 2,000 years ago, when the Bedouins first started breeding their desert war horses.Well the link won't open for me, but I'm assuming it was a long time ago that this happened.
When they first started "Creating" breeds they allowed approved horses to have a full blooded offspring.