I think that the phrase "armchair quarterback" is related to "backseat driver". Wouldn't you other estadounidenses agree with me? That phrase immediately takes me back to my growing up years, and I can see my father on Sunday afternoons, sitting in his chair in the living room, telling the football players on the television how to play the game. I am talking about NFL American football here, of course.

Having said that, I have definitely heard that phrase applied outside the realm of people watching football in their living rooms. If someone sits in the staff room at my school and talks about what the principal ought to be doing, I would accuse them of "armchair quarterbacking".
This is not to be confused with "Monday morning quarterbacking", which is when, on Monday morning, someone can definitively say what the football coaches/players/quarterbacks should have done/decided in the previous days' games. Kind of similar to hindsight being 20/20....... Somebody stop me......