Surely even then the rental contract would specify the equipment they rent, not the space - the data centre could move their rack to a different physical location at any time.
The contract I signed, had a clause that said if they had to move me somewhere else, they would pay all costs of doing so. I don't know how standard a clause this is.
I rent a furnished appartment, and while the company that owns it would never touch it without my permission, the contract is very specific about it being this building, they would never say "mind moving next door?" whereas with a rack in a data centre, not only does the contract not specify exactly where the rack is placed, it makes very little difference about it's exact location.