I will back up and say right after I posted I started thinking about how both systems incorporate fictional positioning in different ways, and that how people interpret what that means seems to lean one way or another based on the game and the person’s sensibilities, so I do think you’re right that it’s not true that OSR does not use it and PbtA does.
Similarly, I will admit I think I’m trying to communicate a not fully articulated thought about the differences between the systems. Things like the example in that blog post of a mathematical rule or formula for fall distance in D&D (1d6 * (# of 10 ft. increments) = consequence), or an equation for how long you can hold your breath, how much you can carry, etc. are what make me think that OSR tends to have people operate mechanically or mathematically rather than “positioning fictionally” (I’ll admit this is probably an arbitrarily skewed interpretation of what the term is supposed to mean). People are given comparatively complex mechanical information and tend to operate on that level, rather than on the fictional, numbers-free or lite level of PbtA. You see it a lot in combat, I think. I tend to fall back on “I use 20 ft. of movement, then I attack (roll…), and then I’ll attack with my offhand (because I have a feat that says I can).”
The contrast in PbtA is the classic “to do it, do it” which tries to get players to speak on a fictional level as often as possible, until the situational queues on the moves trigger. I have to describe the scene, not my interaction with an abstract resource like movement speed (again, thinking of this “positioning fictionally” although I recognize this is a limited interpretation of the phrase). In combat I might say something like “I dash across the room, whirling both blades around towards the knight.” Distance or movement range is sometimes a factor in PbtA games, but only if the DM or group decide to bring conscious attention to it, and it’s easily elided depending on the situation, so it’s a fictional consideration if we’re going to call on a tag or not, versus a hard rule about everything needing to exist in absolute space.
All that being said, I can see how this is actually as OP originally said, almost the opposite of fictional positioning-- it doesn’t matter too much if I established I was within a specific distance from the knight beforehand, we just let the move follow through if it makes sense within established (often nebulously vocalized) fiction. However, everyone at the table would hopefully agree that I’m not allowed to follow that move through if I say, didn’t actually have the swords I claimed to attack with, or had been asleep the whole time. Maybe it’s question of on what level of granularity or attention OSR or PbtA asks you to fictionally position…?
Another example I’ve seen in play (in 5e, for what it’s worth) is when it comes to things like a character trying to assassinate a guard-- the action broke down because we clearly understood the rules for hitting a guard in combat until their HP goes to 0, but we didn’t know a rule for hurting someone outside of combat (was it fair to take someone out in one roll when normally it’d take so many in combat?), and the disconnect between the two caused a problem. We had clearly defined rules for combat, and clearly defined rules out of combat (skill checks), but this didn’t seem to be either, so we decided the action couldn’t follow through.
PbtA encourages you to skip the roll and move through the fiction depending on how interesting people think the situation is, and the moves are supposed to be broad enough to catch any interesting situations you do want to linger on-- if the guard isn’t likely to put up a reasonable fight, you just hurt them, no roll. If there’s a challenge, maybe it’s Go Aggro, but it’s probably not Seize Something by Force yet. There’s nothing stopping people applying a similar philosophy in OSR games, but it’s something that in my experience people who’ve only played D&D are unfamiliar or uncomfortable with.
Now, having typed all those thoughts out, I think it’s probably fair to say that these are all fairly subjective experiences that more reflect a group of middling experience not playing D&D very well, and not something that shows an absolute statement about OSR as a design philosophy =P
For example, I do see how in OSR the fictional positioning (in a broader sense than my instinctive interpretation) still exists-- you can’t hit a thing with a sword unless you’re next to it, so you’ll need to do something about that with your movement action on your turn, etc. I guess what I’m poorly trying to get at is the different forms of conceptualizing and engaging with the action that each system reinforces.
(and apologies for a long, hopefully not too defensive post >.< )