Not true. They can lease buildings and property, however it can be taken away from them at any time. Not a darn thing they can do about it either. Two cases I know of, friends in Puerto Penasco have had a family home there for years, however he cannot renew the lease on the land. He will lose his house in a few years. Also, there were several American "leasers" in Baja a couple of years back who had the threat of losing their homes, because the gov't deemed their leases "illegal". You must be Mexican to own property in Mexico.
Yes, Americans and other foreigners may obtain direct ownership of property in the interior of Mexico. However, under Mexican law, foreigners cannot own property outright within the restricted zone. Instead, a real estate trust must be set up to hold title for the foreigner. Since foreigners are not able to enter into contracts in buy real estate, they must have a bank act on their behalf, much as a trust is use to hold property for minors because they also can not contract. The following is a brief outline of the law regarding such trust, known as "fideicomisos", but potential buyers should always get advice and have all real estate transactions overview by a licensed Mexican attorney.