You're right it varies from state to state, but AFAIK, if you have a right of possession (as a resident does), you can invite others onto the property.
This came up when my uncle had a tenant that rented some warehouse space from him. The tenant had a non-exclusive right to use XXXX square feet of the warehouse. The tenant failed to pay rent and before the right-to-cure period expired, contracted to have movers come and get his stuff. My uncle asked the police if he could prohibit the movers from coming even though the tenant technically still had a right to be there. Their response: Nope, as long as the tenant has a right to be there, he can grant anyone else permission to be there, including the movers.