I love it when I see stuff like this. Well, in my opinion, Remington uses much higher quality steel than Winchester in their barrels. My statement is as fact based as yours, which is to say it ain't. As I recall, Browning recommended against shooting any steel shot in any Belgium made (read FN) shotguns, but the Japanese made ones should be fine with modifed and more open chokes. How does that impact the definition of better? Note, I am not saying there was anything wrong with the Belgian barrels, They were softer than the Japanese barrels, but with lead shot it was a non issue.
Remington did have a batch of barrels that were apparently not up to snuff in some regard. That does not apply to all barrels by a mile. I seriously doubt the Remington 700's downright legendary accuracy is the result of inferior barrels.
OK, Here we go. I participated in a controlled test using a Remington 870 18"bbl Police shotgun and a Winchester defender 18" bbl. Both had cylinder bore barrels. 870 went first. 2 cleaning patches in barrel, half way down, fired 12 ga 2 3/4" slug. No problem. Next cut open slug and force slug halfway down the barrel, fired slug behind it. Barrel blown from breech to muzzle. Lateral split all the way down the barrel.
Defender was next. Patches-slug, no problem. Slug-slug, no problem. Two holes in target. Cut open two slugs and forced both halfway down barrel, fired slug behind them. Three holes in target. Barrel split about 1 1/2" from muzzle back, front sight bead gone. The gun still worked and was still safe to fire even though it patterned poorly afterward.
Is that fact based enough for you? Probably not.
Maybe Remington barrels are better than Winchester barrels but apparently THAT Remington barrel was not better than THAT Winchester barrel.
Knowingly shooting any firearm with a bore obstruction is a very bad idea. I would not worry about a few drops of rain in a barrel especially a shotgun barrel. More than a few drops in the barrel of a high velocity rifle MAY be an entirely different thing.
Belgian barrels and steel shot? I would not shoot steel shot through any shotgun barrel that was not specifically rated for it. Older Belgian barrels that were not made for steel shot should not be used for steel shot.