That seems as though it is probably correct, though using meta-currency as a player doesn't feel to me so much like agency as narrative authority. I don't get to change the direction of the fiction, I just get to change the framing of the scene: I can use a Fate Point (and an Aspect my character has) to turn a random mook into my character's college roommate, but that doesn't define how the fiction progresses outside that scene. The Certificate
@pemerton has mentioned in Prince Valiant, he's described as an auto-win, which seems different (and may be why he doesn't think of it as a metagame instrument/mechanic).
I've done some thinking about it, and I figure that it's my strongly-preferred way to play because I want it to be my character's story, not my story (multiplied by the number of characters/players). It's probably why using meta-currency feels so different to me than operating as my character--the difference between spending a Fate Point to edit an NPC and using a Charm Person spell, more or less. I suspect that makes sense to you. It also, I think, talks to your paragraph below, about tools in the toolbox, which I don't have any strong argument with.
I'm not agreeing with this position, but I believe you have elucidated why it has been said that games that use such metagame rules aren't TRPGs--because they force the players to divorce themselves from their characters, to want something other than what their characters want, to act in the game differently from what their characters arguably should. That has the potential to open a can of worms, so I'm going to say again that it's not my position: I'm perfectly happy to call Blades or Fate or AW or any of the other games that have been mentioned in this thread TRPGs; I don't think they're really operating all that differently, and I don't see any point in defining the category so it only includes games I like.