Why not lie to her about everything and bang her anyway?
Occasionally, though, it does work like you say. I think there was some Asian(?) politician that they tried to blackmail after something like this, and he basically said: "Hey, could you send me a copy of the sex tape? She was smokin' hot, and I'd love to have the video."
https://medium.com/war-is-boring/the-cia-and-kgb-tried-to-bl...
It doesn't even need to be true, just needs to be compelling.