First off, I think not knowing the PCs’ stats is an Iserith thing, not a “middle path” thing. I personally do like to know what all the PCs stats are, cause I find it helps me build challenges appropriate to the party. That said, I do think you’re right on the money in terms of this being the core of our disagreement. I’ve seen it referred to as “challenge the character, not the player” to put a spin on it that favors your style, I’ve described it as placing success and failure on the player’s decisions over random chance, which I think casts my style in a more positive light. But at the end of the day, this is what it’s about, one way or another. Personally, I HATE when the result of the die roll determines what the character does or says. It’s MY character, I should be the one to decide what they do or say, not the dice. If at any point the result of the roll overrides my agency as a player, the dice are overstepping their role, in my opinion. Now, I’m well aware that others feel differently, and that’s fine. Some people find, the idea that the 8-Charisma barbarian could give a stirring speech without having to roll really high just as atrocious as I find the idea that “your character didn’t really say that, you didn’t roll well enough.” And there’s really no reconciling such diametrically opposed playstyles.
EDIT: I will say, I’ve been on the other side of this fence. I used to be very concerned that players being able to do well at things they had low stats in without at least rolling high was tantamount to metagaming, which I just kind of took for granted was a terrible thing. But when I actually tried running the game the way a lot of folks online had been recommending, I found that not only did it not ruin my game to stop worrying about metagaming, it actually made the experience significantly more enjoyable, both for me and for my players. Of course as always, your mileage may vary. But in my personal experience, the game got way better when I stopped trying to maintain a hardline division between player knowledge and character knowledge and police what characters “would do” or “wouldn’t do.”