Andy, I think you're misunderstanding what he's dealing with:
This is an old Evolution design (my Atlas plate is vintage 2006, and has the same mounts). The tube has a threaded stud at one end, and a threaded insert at the other. You put one nutsert into the frame of the car, and then screw the stud end of the tube into it until it's tight against the frame (then repeat on the other side). Then you lift the plate into position, which aligns holes in the plate with the threaded insert at the bottom of the tube. A bolt (with washer) then passes through the hole in the plate and threads into the insert in the tube to secure the plate. If memory serves (I installed my plate 15 years ago, so I'm working from OLD memory here), the stud appeared to be pressed into the tube, so you can't just unscrew the tube from the stud either - for good or ill, the tube and stud are one assembly and will NOT come apart easily.
The "tube" to body/frame is a blind attachment - the stud connecting the tube to the frame is completely hidden by the tube, and there's no access into the frame cavity to get pliers on the nutsert unless he starts cutting into the car's frame around where tube is attached.
The problem the O/P is having is not getting the plate off the bottom of the tube (which your "grinding off the head of the bolt" suggestion applies to), it's that when he tries to unscrew the tube from the nutsert in the frame, the nutsert is spinning instead of gripping the frame metal and allowing the tube (and, more importantly, the stud installed in the tube) to spin within the nutsert. This is why I and a couple others have suggested trying to put sideways pressure on the tube (as if you were trying to bend the bit of the frame it's connected to) in order to try and force the nutsert to bite enough to let him get the two apart. If he's unable to immobilize the nutsert via sideways pressure/prying while unscrewing, there's only one other option - cut out the bit of the car's frame where the nutsert is, and unscrew it once the whole thing's out of the car.
To the O/P you referred to the car you're taking the plate from as "RIP" - is cutting into it to allow access to the nutsert directly (or to cut around it so the bit the nutsert is installed in drops completely out of the car, leaving a hole) an option?