Right you all are, but modern guns are made with modern steels. Many of out ML'ing barrels are 12L14 steel, which isn't as tough.
That said, a cut-in barrel lug or sight is going to have most of that cut away steel replaced by the lug base, so much of what is lost is then replaced. If you solder the lugs back in place I'm guessing most all of the lost strength is regained. As the thinnest part of the barrel is the mid point of the barrel flat, there will also be something of a "spine" put there as well which is the vertical part of the barrel lug. Soooo, all that said, in several places on the forum I've seem 0.008" mentioned as the absolute minimum, but 0.010" and 0.012" are mentioned more often.
You also have to remember that the further you get down the bore, the lower the pressure will be. Ex; a 24" M1 Grand starts at ~48,000 psi at the breech, but that pressure has dropped to <5000 psi 22" down the bore (5% of breech pressure) where the gas port is. Most of our heavy loads with BP don't generate much more than 20,000 psi (at the breech), so assuming a level linear pressure drop as you go further down bore you can do the math at your target location as to your expected pressure.
It's for subjects like this that I really wish Zonie's was around to answer them. He had all the metallurgical data and fail point pressures right at his finger tips. If you research some of his old posts you may get some more educated data.