That’s not always true.
For the cheaper shotguns, yes, it might be true that the damascus barrels will let go.
For higher quality shotguns, their damascus can be stronger than the “fluid steel” of the day.
See WW Greener’s writings on the topic for more information. He had proofed some of his firm’s (WW Greener) damascus barrels and had the proof house feed the same loads into fluid steel shotguns of the competition, which caused ruptures.
There were several grades of damascus steel back then. Yes, there are lots of no-name Liege tubes that would probably fail, but the higher end shotguns (both American and British) of the era had higher quality barrels than the no-name twist steels out of Liege.
It's not about how strong the barrels were when they were made. I agree with the relative strength THEN. Damascus barrels were actually superior barrels when new than many cold rolled welded barrels and hammered steel barrels. BUT, and it is a big but, over time the discontinuities in the Damascus barrel forging technique allows for internal corrosion to form in the hammered wire forging that that forms the Damascus barrels. This corrosion between the mechanical/welded/pressure joining of the metals that are at the core of all damascene metals is unavoidable, weakening the mechanical welded heat bonding because oxygen is incorporated in the joint by its very nature. . . starting the formation of rust at the creation of the barrel. With age, all damascene barrels LOSE considerable strength.
Barrels in that period were ALL proof tested with black powders that were far less pressure producing and slower burning than modern faster burning, higher pressure producing smokeless shotgun powders. Now add the corrosive nature of black powder and the even greater corrosiveness of the fulminate of mercury primers used during the useful life of most of these damascene barrels and its effects on accelerating the corrosion between the domains of the metal in those much more porous barrels. Shooting shotguns with Damascus barrels with modern loads is NEVER advised.
I am past manager of the Olde Sacramento Armoury and I was the appraiser and buyer of used and antique firearms for Simms Hardware's Gun Department — which was named #1 Gun Dealer in the United States in 1971. . . and was a qualified expert in the California Courts on the identification and values of Antique firearms back in the 70s. We labeled every damascene barreled shotgun a wall hanger, a non-shooting relic and instructed all sales people to instruct buyers that they were never to try shooting them as they were considered unsafe. We had several "educational pieces" on hand with blown chambers to show them what would happen if they tried. A couple of those looked brand new. . . and were made by some of those "top names" in gun making from London and New York. They still blew.
By-the-way, I CRINGE every time I see the people on Pawn Stars shooting fine antique firearms, claiming they have a greater value if they are "fireable!" Every time one fires a vintage gun, one takes the risk of breaking, damaging, or destroying it. . . and more wear is added, degrading the value of the gun. Operation, timing, etc.,condition, are ALL determinable by examination by a qualified expert without the weapon being fired. I've seen their "expert" dry firing a percussion Colt revolver onto the vintage, original percussion cap nipples without protective covers, which will damage both the nipples and the hammer, demonstrating his complete lack of proper handling knowledge of even NEW percussion guns, let alone valuable antiques! Aaaarrrrggghhh!!!!