Have you ever heard of bending an Upper receiver?

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Well, since everyone seems to be chiming in.LOL

Heres my opinion:

A barrel nut screws on to the receiver. Period. If you lube the receiver threads and the front of the barrel extension, almost every single drop of torque is directly between the barrel nut and the receiver threads. Using a clamshell or cutting boards keeps it there. I use a clamshell with an anti-crush insert.

When you use a "reaction rod" you are no longer supporting the receiver at all. You are fixing the barrel extension in place. The barrel extension isn't receiving the barrel nut, the receiver is... When you torque the barrel nut onto the receiver threads, the receiver tries to turn (communicating the torque on down the line). The only thing resisting that torque is the barrel extension's index pin. Otherwise your receiver would simply spin in circles.

Using the other Brownell's rod (while fixing the barrel nut wrench in a vise) does the exact same thing in the opposite direction. The rod turns the barrel extension. The barrel extension would then simply spin forever unless that rotational torque is then transmitted to the receiver by the index pin. The index pin spins the receiver, and the receiver (where the threads are--- not on the barrel extension) gets torqued into the barrel nut.

Whichever rod you use, it transmits torque through the receiver via the barrel extension index pin. There's absolutely no way around that.