When I was a troubled teen, access to LGBT stuff on FidoNet / the Internet is probably the main thing that kept me from suicide.
Blocking access isn't the answer, unless you want to either: a) exacerbate their issues or b) give them a crash course in black-hat networking techniques. Tread carefully, and consider that the family (your friend) may be part of the underlying problem.
This isn't a Ctrl-Alt-Del question, IMHO.
I think the distinction is between material that may cause further harm as opposed to that which could be used more in a supportive context. That's clearly not a black line but a very grey one. I absolutely agree it's not a ctrl-alt-delete question.
I can understand why they would want to filter out extreme, unfiltered, content, or at least make it harder to get at.
He says "No I'm sure we'll never stop her, but we have been very trusting - too trusting perhaps so we have to take control. Some of the stuff she has been looking at is hard for us to process, never mind a 13 year old."
I think part of is trying to better ensure that content is age appropriate. As we all know the internet is home to extreme views from any subject you care to mention, much of it not suitable for children. Much like films have an age rating on them, so too should some of the internet.
I really don't know the answer to a lot of this, it's not a problem my parents had to face when I was young and one that I have not yet had to face with my own kids who are currently still very young.