It's just the fact that shows that you trust your children. Parents should trust their children, and give them a chance. If you find that your child has been chatting with someone they shouldn't or watching pron, or doing other things that they shouldn't, then move the computer back into a public area, and keep it out there until you have rebuilt the trust between you and your child.
Teens shouldn't have free run, but they should be trusted, and given some privacy. As I said earlier, young kids should be supervised when using a computer, but there is absolutely no reason to watch everything a teen does on the computer. I'm fine with weekly or monthly internet history checks etc. even though my parents don't preform them. They no longer check in on me, because they trust me, and because I haven't violated that trust.
Don