Barrel material is not the only consideration.
The mechanical structure of a double rifle's (or combination/cape/vierling/drilling/etc) barrels (a weldment essentially) bring some specific and local restraint and stress-risers to the barrel tubes.

With ribs, wedges, etc, firmly (by design permanently) attached to the barrels, their expression of the 'donut wave' energy which occurs during the event phrase of internal ballistics is restrained for a portion of the barrel's radial section.
Furthermore, at the various seams (which are functionally stress-risers) there are distinct heat-effected zones.

Chew on that.

Via anecdotal study and discussion, the OSR syndrome appears to be *LOCALIZED* (along the helical path of rifling, in a helical banded pattern, duplicating the array of rifling) expression of excursions beyond elastic limit that print a pattern or optical effect on the exterior of the barrel surface.
This would definitely account for the transformation of the metal's characteristics (change of regulation, loss of accuracy...) WHILE maintaining relatively sound mechanical performance (the barrels don't completely bulge or blow) at the same time.

Acceleration is serious business.
We're talking Einstein shit here and those skinny barrel walls are seeing more and more force per area unit as the bullet cruises down the tube towards the muzzle.
More barrel tends to equal more velocity per given cartridge load!
That could have something to do with OSR showing up 'less near the breech, more near the muzzle' if that's the case.

If anyone here has a relationship with Werner Mehl or Kurzzeit (or wants to start one), that would be a good facility to consider for photo/video-documenting this phenomenon.
They already have the equipment.
It appears as if they have the interest in video-documenting the destruction of firearms and projectiles.

There is plenty of conviction, some available resource, and the possibility of some commercial industry participation to the point where the issue might even end up getting current technology in the pursuit of positively documenting this OSR business for those who will need 'picture-proof' of the 'Hard Monolithic Solid + (Classic or modern, *properly struck*) Double Rifle = OSR' recipe.
That might help settle the issue for another 20 years.

Cheers
Tinker