It is possible that there were horses still here in the US prior to the Spanish coming here but they were likely not Appys. But a pony similar to the UK Exmoor. The Exmoor pony has a unique jaw feature which has been found in older fossils remains in the US leading many experts to believe that this is where the pony originated in its more prehistoric form. The breed also has other primitive characteristics such as the make up of its coat, the heavy bony ridge above the eyes
Its said that the horse disappeared from the US where it evolved 60 million years ago at about the same time as humans entered it, crossing the Bering Straits and going in opposite directions and as the Indians themselves seemed to have little knowledge of horses when the Spanish arrived it was assumed they hunted what were left to extinction - that might not have been the case though and the large ridden Spanish horses would have looked very different to the small rough hairy ponies they saw only as a food source.
Spotted ponies were commonplace in European history and the cave paintings in France that depict them date back to c.25000 years ago, Europeans also traded with the Chinese and the spotted horses from that region became highly prized by the Spanish so I think that they are the most likely source of the appaloosa.
Let me repeat...there is absolutely no evidence - nada - that horses lived in North America between 10,000 years ago until the Spanish arrived...no fossils, no myths, no legends...nothing. There was no "mystery pony" that survived and lived nearly 9,000 years, leaving no evidence.
However, your conclusion is absolutely logical and correct...Spanish Jennets, from which the original Appys and of course Pasos are descended, originated primarily from far eastern Asian horses with some unknowns mixed in - probably Barbs.
Some people, myself included, believe that the original Appys bred by the Nez Perce WERE Spanish Jennets period - later crossed with drafts and other horses that became available, that changed the Appy from its original light and rangey conformation to a thicker stockier conformation, and then even later crossed to produce a stock breed by the white man, resulting in the typical modern Appy we see today. True foundation Appy breeders produce the intermediate Appy - the thicker type with draft blood, but I know of nowhere that you can find an Appy that is so pure as to justify being labeled an "original" Appy/Spanish Jennet...the same being said for the now extinct Spanish Jennet itself, that is in the process of being recreated as closely as possible...