They can do whatever you presume the rich birth tourist does, like deposit in foreign banks, not own US land, obfuscate land ownership through trusts or straw owners.
It appears your argument is that foreigners are greedy, lazy, fraudulent, exploitative, and shameless, but Real Americans never stoop that low. Again, do you have statistics on this, or is just kind of a feeling?
If your answer is dual citizenship giving them access to banks abroad, a wealthy American can buy another citizenship.
There is nothing to stop them from just not owning a mortgage or house, since that is the thing you say will catch them.