[chii]

> but one or the other must be true.

they are neither mutually exclusive, nor even related.

You have a key that opens a door to a house you dont own. Do you have permission, just because you got a key, to go in?

You lost a key to a house you have already been given permission to go in. You found out that there's actually a master key that you can get in the black market, which you buy to open that door to go into the house.

[dijit]

Alternatively: I lost the key to my home (which is rented) and someone is able to fashion a functioning key.

That's actually legal.