Have you ever heard of bending an Upper receiver?

[Ullr]

Of course there is torque applied directly at the threads.

In this case, "directly at the threads" means directly to the barrel pin and receiver notch.

As for the pin notch, I put grease between the barrel and the nut so any twisting of the barrel is minimized,...

Greasing the interface between the barrel and the nut reduces torque transfer between the barrel and the nut. That has no bearing on the pin notch, which is part of the receiver. Nor does it have any bearing on the torque transfer between the barrel and the receiver , which occurs principally via that notch. You cannot reduce torque transfer from the barrel to the receiver if you are going to use a reaction rod type tool. Transferring torque to the receiver via the barrel is how the reaction rod works.

... and there is certainly no more stress on that area than with any other method.

Of course there is. The typical clamshell or receiver-insert type tools do not directly stress the barrel at all. The only twisting force that the barrel (and thus the barrel pin and notch) receives when removing a barrel nut using those tools is by friction transfer from the barrel nut to the face of the barrel extension. As you point out, that minimal force is further reduced by the barrel nut grease. The resulting force is small, and that small force is what the barrel pin and notch were designed to resist.

Using a reaction rod tool, the 30-80 ft-lbs of barrel nut/receiver torque is being applied principally to that notch by that pin. Similarly, that same torque (in magnitude - the direction is opposite) is typically applied to the barrel nut via larger notches by a wrench with more and larger pins. Given that I have broken the 3/16 steel pins on barrel wrenches and stripped notches on steel barrel nuts while attempting to remove stuck barrel nuts, I wonder at the advisability of performing that operation via a single 1/8 barrel pin and matching receiver notch. Wrenches and nuts are cheaper than receivers and barrels.

Torque is torque regardless what it passes through.

Indeed. And that is my point. Contrary to your previous assertion (now edited away ...) it is not the case that the receiver is not stressed at all when using a reaction rod tool. Rather the receiver is stressed exactly the same amount. The difference is that the stress which creates the torque is concentrated on a much smaller area of the receiver. That has some potential benefits, as you point out. It also has some potential drawbacks.

My intent here was to bring this particular tool into the discussion,...

And here we are, discussing that particular tool. Mission accomplished

BTW, I edited my op to say "body of the receiver", which I thought was the subject of this thread anyway.

And you changed the text of this post as well. The point of my OP was to correct the error of the now edited statement...

The subject of the thread is damaging receivers when removing hard stuck barrel nuts. For the reasons stated above, the reaction rod type tools would seem to bring that risk to that task.

Good discussion.