It seems that whenever the subject of forging barrels comes up it is assumed there is only one way it was done in the day. That is, form a long, slender piece of metal, thicker on one end and tapered. This is heated by small sections and progressively bent and welded into a long tube, with a seam the full length on one side. It's true that was done, but there are other more complex ways. One British and Spanish method was to form straight rods of metal about 2 feet long, 1/2" wide and of different thicknesses. These were heated and forged in a spiral fashion around a properly sized mandrel and welded into one piece. About four of these were made, of appropriate thickness depending on where it was in the barrel. Then all four were welded together successively to form a tube. From there the reaming, shaping, filing, turning on the lathe or whatever were basically the same as with the tube made of a single piece of iron. The British called these twisted barrels, the Spanish called them wrapped barrels. The single piece barrels were called common barrels. These twisted barrels were of a much higher quality than the common ones.
It would seem that many of the suggested reasons for swamped barrels being made that way would be precluded by these methods of making them. I've read a lot about how barrels were made in the day, British, Spanish and Portuguese, and I'm of the opinion they made them exactly as they intended, accidental swamping wasn't a thing. In the 1718 Portuguese book The Perfect Gun the actual dimensions of barrels are given, and they were swamped. On purpose.
Spence