Apparently the poskim I cited (I don’t know if there are any opposing view), hold that sometimes you do know for sure. And otherwise you need to give it.
I also don’t agree with you that following the tochocho as halacha describes it to be given (including possibly public humiliation if it didn’t help after giving it privately), will be ineffective. There are other circumstances even today (i.e. with the get issue) where public humiliation is utilized. Is that always ineffective iyo?