The rules for Recovering Lost Cohesion (p. 212) state that the Kill Team regains one point of Cohesion when "Any member of the Kill Team spends a Fate Point". Taken at face value, I read this to mean that any time a player has his character spend a Fate Point to gain one of the benefits listed under Using Fate Points (p. 204), so that's how we've played it. Since we have rather large group and our sessions don't really last that long, our current adventure has seen a steady increase in the Cohesion stack.
However, the Back Banner Wargear item (p. 171) seems to suggest something else: "When a Kill Team's leader spends a Fate Point to restore a point of Cohesion, he restores one bonus point of lost Cohesion if he is wearing a Back Banner."
Does this mean that we've been playing it wrong, and that in fact the Battle Brothers need to spend Fate Points to specifically regain Cohesion, rather than this being a side effect of them spending Fate Points for other purposes?