I don't believe American's can own property in Mexico. You get a long lease. I could be wrong but the point is there is no equal reciprocity or quid pro quid with Mexican law for Americans.
A bunch of seniors bought homes just south of the border in CA - within months the Mexican govt came and kicked them out and took their homes away. They had some kind of deed but it was judged to be invalid. Some of the seniors lost most of their savings.
You are right. The United States is one of only a few countires where you do not have to be a citizen to own property.