Of course you can blow a shot gun up. Bad reloads maybe. A bore obstruction is probably the most common cause. A bad reload that leaves a wad in the bore will usually just dog knot the barrel at the point of the obstruction. A glob of snow or mud in the muzzle will banana peel the muzzle very nicely. Those shotguns are neat conversation pieces and will usually stand on their muzzles after that
A 20 ga loaded
under a 12 ga will usually rupture the chamber as will a 28 ga
under a 16 ga.
A slam firing or out of battery firing Remington 1100 or 870 is particularly nasty to anyone standing on the port side of it. Usually not catastrophic, but small particles of brass head, hull or carbon spewing out the port not to mention the high velocity gas... not good things. But rattly hinge, break action shotguns don't fail the way of the malfunctioning auto loaders or pumps do. About the only way they catastrophically fail is by something that causes a very high pressure/kinetic event, commonly a substantial bore obstruction near the chamber.
In a previous life I tested and documented some of the ways guns fail, including some shotguns. One of the most difficult to purposefully blow up was a hinge break action shotgun. We are talking smokeless/nitro proofed guns here, not soft iron black powder designs with laminated/twist steel barrels. For smokeless/nitro proofed shotguns with hinge actions, the barrel may set back from the breech face and spew gas with extremely high pressure loads, but compared to other types of actions that could shear breech locking mechanisms, it is very difficult to make the hinge actions fail catastrophically before the chamber ruptures.
Additionally, a smokeless proofed .410 hinge action common factory gun built on a full sized platform was nearly impossible to blow up... at least up to pressure levels that I could produce with any possible overload or load combination. These likely exceeded 100kpsi. They would spring the actions open enough to relieve gas pressure but neither the hinge system nor the chambers would come apart (catastrophically fail).
Anecdotally, I grew up shooting a rattly hinge action single shot 16 ga I found. Factory records indicate it was made between 1898 and 1915. I found it in rusty and somewhat pitted condition behind our farm when I was 9 years old. My dad took it to the only gunsmith available and I was given the ok to shoot and hunt birds with it. It was just as rattly when I found it 62 years ago, as it is today. It has shot upwards of a couple thousand rounds over the years. In about 1961, IIRC, It's firing pin broke and it was the first real gun I fixed by myself. At age 12, I made a new firing pin from scratch and it still has that firing pin today. I shoot it once a while and took it to the range a couple of weeks ago and fired 4 shots into a large paper backer to check pattern.... I hadn't done that in a long time. Why shoot it?... just because.
This is a true anecdote, as so many stories are on internet forums, which doesn't prove a thing about the Belgian double in the OP. But I am much more leery of getting hit by shrapnel of a failed gun fired by some idiot reloader on the bench next to me testing his new mega hypersonic loads in his boomer rifle than I am shooting regular factory ammo in a proofed, hinge action shotgun, rattly or not.
Here's the Hopkins and Allen 16 ga in the anecdote. Note the small gap in breech- bottom pic
