Yes it was Transocean's rig, nobody is denying that - however BP leased the rig and was the sole driver of it.

No, you keep saying that but it's wrong - the rig was staffed by Transocean workers.

Under their lease agreement BP was in full charge of the rig and its safe operations, hence the reason why BP was able to over ride TransOceans safety procedures.

Override there unsafe procedures, more like.

If you rented a car from Hertz, and you were careless driving it, you would blame Hertz wouldn't you.

That's right... I'd blame 'em for hidden defects and of course if they provided the chaeffeur who didn't know how to drive I'd sue their ass for that as well.