Nah, it's all legal. Companies buy land legally via dummy corporations all the time, for good reason.
A dummy (shell or front) corporation is still a legal entity (although if that is not done correctly, it could be illegal- remember part of the Clinton Whitewater scandal was the McDougals created a fake shell company to hide financial transactions.) That is completely different from providing a false name- a fake personal identity can't be used as a 'front' for a legal document.
In other words, I can create a LLC out of the blue to buy a property.
I can't, however, claim my name is Ronald McDonald and buy property under that.
As I mentioned, part of the Whitewater scandal was using a fake corporation to buy property to hide where the money came from (false inflation of value as property was being sold, just to the owners themselves using the front).
If we didn't accept this from the Clintons, why would we think it is OK because this time the guy who temporarily has an R behind his name does it?