I would say that it is pure BS. When you rent, you are seized of the property and have all rights to it as if you owned it. Similar to "special bailee" rights. What if they said no bible? No landscape paintings? Research state laws--search under "renters rights, landlord restrictions, etc" and I'm sure you can come up with a statute protecting your right to have anything, legal, within your property.
In general, a special bailee has all rights to a property, real or chattel, except to those who actually own it. The owner transfers his rights through a vehicle, viz., a lease. Short of selling your apartment to somebody, you have rights as if you actually owned it. Quote from Common Law:
"The test of the theory of possession which prevails in any system of law is to be found in its mode of dealing who have a thing within their power, but not own it, or assert the position of an owner for with regard to it, bailees, in a word. It is therefore, as a preliminary to understanding the common-law theory of possession, to study the common law with regard to bailees. "