Either way it does not matter as it is a matter of symantics. I could turn round and say I am doing it to protect my child, if I had any, and they could turn round and say I was being nosey.
They are paying for the connection, and most probably the phone line too. If s/he is doing something he doesn't want their parents to see then they shouldn't be doing it. I was raised with a major golden rule, if I would be ashamed of anyone seeing/finding out about it I shouldn't have/be doing it.
While living in a parents house you live by their rules, if you don't like it....
reason, who pays the ISP and phone lline bill? After all it's the name on the account that gets into trouble regardless of how old you are.