the only possible flaw in your logic may be altitude. They originated in the andes, which is the southern extension of the North American Rockies. It could be 10, 20, 30 degrees or colder in a mountain valley thats 10,000 feet above sea level. I dont have an exact figure but i know it gets below freezing at the summits, otherwise the snow caps would not be possible.
Thats more than enough to make equatorial temperatures tame enough for a heat sensitive crop.
makes Chile and Argentina seem a lot more like Maine or Idaho in terms of temperature.
