What I meant by "ownership" is that the building, or at least part of the building is owned by the company. I should have phrased it better. Lets give it another go:
The company should be in direct control of the management of "their portion" of the building. They should be free to drill holes in the wall and do whatever they need to do to make the datacenter fully functional and as versitile as possible. It definately helps if they own the building, because they will be free to do whatever they need to do such as knock out walls, build additions, etc, but it is not necessary that the company own the building itself, but it is unfair to have a closet in your office building and hook it up to a T1 and an APC battery and call it a datacenter.
Hope that clarifies it a bit!