While any foreigner can come to the US and purchase real estate and the same bundle of rights as that of US citizens, US citizens are not given the same rights abroad.
Mexico requires US citizens to hold ownership in a trust, incurring annual trust fund fees in addition to property taxes. Vietnam requires an in country job and if you loose that job you are required to sell, thus creating an unfair advantage.
The most used reason for this is that if US citizens were allowed to own property it would raise the cost of housing and make it impossible for the average person to own a home.
Malaysia allows foreign ownership but only on homes priced above $150,000. Not only does this invite foreign investment it also protects lower income properties.