The other beautiful part is that people won't believe you (if you tell them CIA has stalked you or approached you) - this only keeps you quiet if you actually give a shit what people think - to mitigate this practice not giving a fuck - it's great for your skin too

If it feels too good to be true, it probably is. Nothing is actually a done deal until it's in writing with a witness and notorized... Or a lawyer present.

It only looks bad to certain types of bosses that you were approached.

It really depends. Like let's say I'm the head of the KGB and one of my employees was made by the CIA - guess what?! Now you're tasty bait.