Interesting idea. I did some searching and most web sites claim peaches were first cultivated in China about 4000 years ago. They were transported west along the silk road and became established in Persia where Europeans discovered them. Then the Spanish brought them to the Americas. [www.uga.edu]

It would be interesting to get more info from your source in the Park Service.
If the first Spanish missionaries brought peaches to the Southwest by around 1550AD it is possible that the Navajo could have been cultivating them for some 280 years before Kit Carson.