The key would be one of several things the contract would address. Pretend like you are trying to explain to your brother-in-law why, no matter what happens, it's not your fault. First draft:
There is one key to your storage box. The key belongs to the storage facility. If this storage box was rented to someone else in the past the lock was changed to accomodate this key before we rented the box to you. Like the key to your home or your car, this key controls access to an otherwise secure place. Do not lose the key. Do not make a copy of the key. It is the key that controls access to your storage box, not the storage facility. You are solely responsible if the key is used to obtain access to the storage box by anyone but you regardless of the circumstances under which that person obtained the key.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.