And that alone makes them at least partly responsible.That's already where you are dead wrong. Lot of parents know shit about their own children.
It certainly doesn't help if you have a d(e)ad who tells you he's gonna kill you if you turn out gay one day.
I've heard horror stories from gay people, you cannot believe the shit they sometimes have to go through. Still, I don't think if you kill yourself, it's automatically the parents fault.
So many instances are "at fault" when someone commits suicide, it's hard to point a finger at someone specific in most cases, unless it's a clear case of mental and/or physical abuse by someone.
I still cannot understand why someone would commit suicide. Just move away, surround yourself with new people. Leave shit holes behind you and start a new life, even if you are 14 you can always just move away and get institutional help.
It's not like LGBT people who aren't accepted always have incurable crippling depression.