Ill step in to this thread, as a parent. No we do not know for sure everything you are doing. Even when we think we know, we arn't 100% sure. We can be fooled if we dont want to think you are doing something. I am pretty pc savy (more so then my 13 year old son anyway) so I am confident that I know what he is browsing on the net without having installed any sofware ... yet anyway.
I do find questionable things in his history after him and his friends have been in the office alone for a while, but so far nothing that I thought I needed to yell at him for.
But over all, parents are not as confident as we seem to be and can be convinced of just about anything so long as you dont have a proven history of poor judgment.
Hope that helps