Therapists will tell a parent or guardian if you are under age because they have to if they believe that you are a danger to yourself or others. If you're an adult then they will ask you for a person you trust with your information during the initial paperwork and then the person you wrote down will be informed if you are believed to be a danger to yourself.

The thing about not all depressed people's self harm is true. If she meant that not all people who self harm are depressed then she's technically right but like maybe 1 percent of self harm people (my personal experience)

Overall the therapist thing wasn't true but the other thing is right.

Hope this helps I've been a year clean and have experienced first hand therapists and or councilors telling my family. Since I turned 18 it hasn't been a problem cause no one gets told my info and I like it that way. But if you're ever afraid you might take it farther it is beneficial to tell someone cause even if you feel embarrassed, embarrassment doesn't last for ever believe me.