I think you are projecting the sense of the word from computer security onto people. But "vulnerability" always has that second sense in common speech, as in "showing vulnerability". If a person is actually open to being harmed in some way we use the phrasing "they are vulnerable to ...", which has quite a different meaning.
No, definitely not thinking in computer terms. I know the word from a completely different context. I think what they mean is sensitivity (which can be good or bad) and tenderness (which is generally good). But there are contexts in which it is not helpful. We have a problem with street violence where I live, and showing your emotional side to a potential attacker is not the best way of avoiding trouble.
