and vice versa
Yes, thats true, I think its part of the reason, they still instruct women, or really anyone in trouble, to scream FIRE, instead of help, because they realize not many people will come to a yell for help, but for fire, people come running.
I think it’s why most manager training emphasizes being incredibly careful about what you say around women so they don’t misinterpret politeness as an overture. And make sure one is never alone with a female, particularly a subordinate, even for matters requiring privacy make sure the office door is open and you’re visible to folks outside the office. Never offer a female co-worker a ride alone, never accept a ride from a female co-worker. That kind of thing. Don’t risk an offhand or polite comment being interpreted as something more sinister.