IANAL, Even if that is true, the router is rented, so it belongs while he pays his connection. In my country and I think in most countries, a landlord can't enter in any of his rented houses without consent of the people who live there. By your way of thinking Verizon could enter your network even if you protected it, just because they own the router.
Verizon still owns the router. To use your apartment analogy, just because you rent an apartment, does that give you the right to change out the locks and not give the landlord a copy of the new key?