To reinforce the OP's point with the first game listed here (I'm a player), the first clock was dangerously close to failing, with the Editor continually slamming our very criminal enterprise with evidence of it's criminality while we tried to pretend to be legit and innocent "wrong place right time" good Samaritans. This further escalated when one of the characters tried to act offended about a slight, and failed, letting the Editor really get up on a strong horse to pretty much satisfy herself that we were what she thought and she could run the story. She was on a roll, things looked bad, and my character went all out with a hail mary pass, trying to head everything off by basically pounding the table ("If the law is on your side, pound the law, if the facts on on your side, pound the facts, if neither are on your side, pound the table"). I effectively initiated a walkout, stating that she's obvious more interested in proving her assumptions about honest working men so she could slander them than finding out what's actually happening in the labor conflict -- and how various upstanding members of Coalridge are involved in some very shady things. Our third player immediately jumped in with an assist, suggesting that, since the Editor already knows he's a member of an upstanding family in Duskvol, that running with her current story would mean he'd be very keen to follow up on the slander charges. The goal here was to play on her curiosity that we had some real dirt -- that there were serious targets for expose rather than just another small time gang trying to make a move, and assisted by the threat of legal action.
Okay, so, stepping back, here, NONE of this was established -- there was no stated curiosity by the Editor, nor was the threat of legal action understood to be actually threatening. The mechanics here would establish this. And, according to those mechanics, the results would have been catastrophic on a failure. Luckily, with the added die from the assist, this turned out to be a critical success (2 sixes rolled) and the Editor backed down and exposed a deep curiosity in our story, which lead to the closing of this clock (the 5 ticks from the critical did the trick) and the opening of the next.
So, what happened her is that a deeply suspicious NPC was converted to being interested and much less suspicious through an action. This is exactly what the OP is asking for -- how do these things work. What's notable in Blades is that this action is mediated by the current fiction and the mechanics of the game only -- the GM has no presumption of NPC beliefs, traits, or thinking other than what's been established in play. There are other systems that do this, but it's very much contrasted by the D&D-alike approach where the likelihood of this working is entirely up to the GM, and what they think is possible.