I haven't managed to clarify the rules regarding the Counterintelligence card. Is says "when any threat..." Shouldn't it cancel the threat placed at the beginning of the villain phase? Right before the villain gets to act? Because threat is placed then... in which case the card would only be remotely useful and only in multiplayer (though 2 cost for 2 threat is nothing to write home about) further getting better with more players, as threat scales, usually, 1/player. It is also not worded as optional so you can't hold on to it up to a moment when the villain would scheme heavily.
It's not "forced" so I think you can choose when to activate it, so it'd be most efficient to save it for when the villain is scheming for 3+. If the card had a "forced" syntax, then I'd interpret it the way you asked your question and be forced to using during the first part of the enemy phase when you add threat to the main scheme.
Somehow I got my hands on this a few weeks ago already. It's the only hero pack I really dislike. It feels so passive, as most what you're doing completely depends on what's revealed. Sure, "Preperation" fits perfectly, but at least to me it just doesn't feel good. I've got a bunch of Prep cards laying there and "waiting" for them to trigger. As Wossy says, you don't do a lot, the boss isn't doing a lot as you prevent them from doing so. To me it feels pretty boring to have nothing happen, even if that renders me virtually invincible, especially solo.