What he said. I guess it would be just like them saying you cannot smoke, have pets and so on. They are not banning or discriminating against smokers or pet owners just simply the cigarettes or pets being on the premises.
It is still their property, however, their powers are constrained by contract, i.e. your lease agreement. Now, if there were a clause in said agreement banning firearms, they would be within their rights. You, of course, would be within your rights to not sign that contract.