The paragraph after your quote does call it a "one-shift hit"
Right. A "one-shift hit", not a "one-stress hit". Consider the baseline rules for attacks: you do a contested roll to determine if there's a hit, and if so how many shifts the attacker gets for the attack. You then translate shifts into stress by adding weapon rating and subtracting armor (and maybe adding other modifiers, such as for Strength powers or stunts). So by saying that the grappler gets "an unopposed attack ... which has a value of one shift" or can "inflict a one-shift hit", the wording implies that this is an attack that is assumed to hack skipped the contested roll and gets an automatic one-shift result. Then it seems as though you'd translate this into stress by adding (appropriate) weapons and subtracting armor. (Note that "Any successful attack adds the weapon value to the stress inflicted, but subtracts any relevant
armor value" (YS202) and the grapple rules indicate that this is in fact an attack that has succeeded to the tune of one shift).
I hadn't noticed this before, and to be honest I'm not sure that this is what the designers intended, but it does seem to be what it says -- and I can't see any alternate wording in related sections that would lead to a different conclusion (which is known to happen from time to time in the RAW). If it had been worded as "inflicting one stress", then I'd go with that, since weapons only affect
attacks. As a side effect, this also seems to mean that someone with mundane armor may or may not reduce the stress depending on whether the means of inflicting the damage would make the armor useful (I've kind of assumed all along that Toughness powers would apply, making a character possessing them largely immune to grapple damage from characters without a grapple damage bonus).
Aha! As I'm writing this and looking through the rules, I think I've found a loophole that probably counter my argument. You see, grapples are governed by
Might. And Might does not include trappings for any weaponry, so technically the weapon ratings wouldn't apply. Unless, of course, you had a stunt that either allowed you to add a weapon trapping to Might, or to grapple using a skill that had a weapon trapping. Of course, this still leaves the question of whether armor rating (particular
Still, I like the idea; it might be worth working into a house rule of some sort (or a stunt).