I realize the topic got off to Hoop Stress and I think I understand that is about internal force pushing out and around the cylinder, but I also think I understand what point Tony is getting at as well (don't want to speak for him so I will ask in my own way). I think we may be debating apples to oranges a bit, but also don't understand how the cylindrical stress impacts the vertical stress where the barrel meets the action.
If we ignore the pressure from the cartridge being ignited and pushing out against action (what I see as Hoop stress), there is certainly still a force being applied in an upward direction where the tenon meets the action. At it's simplest, its a an equal and opposite force calculation based on how long the barrel is, it's weight, etc.
To me there would be three main outside aspects that then would affect this joints rigidity (and ability to counteract this vertical stress). One is the type and number of threads per inch and how much force this counteracts. I suppose in a perfect fit, this is more about horizontal force as it pulls shoulder against the face of the action. 2nd would be how much of that force is managed by the shoulder against the face of the action. And third, how much of that force is then also spread to the walls of the action where it threads in. I suspect this force actually utilizes much more of the action length than just the joint length itself.
It would appear that all else being equal, and assuming for example the action is bolted into an immovable mount (just for arguments sake) that if one was to apply force on the end of the barrel in the vertical plane, then it would seem that an action with a thinner wall would not be able to counteract as much force as that with a thicker wall before some type of deformation would take place. I don't think this is really a big surprise.
Now, the question then becomes, is there ever enough force applied through gravity to a barrel to make this a real issue assuming proper fit of threading specs, tenon length, etc based on the material being used? I don't know the answer to that question, but it's clear that Mike doesn't think it does or I don't think he would have done what he did.
With that being said and I think the question some would like to understand is what Advantage does the larger tenon diameter provide that the smaller doesn't. I think that may be proprietary, but trying to get to the real root of the questions.