Of course it is a parent's responsibility, but it would be nice if others were willing to help if they have that ability. If Apple are going to allow applications into a store with an age rating of 4+, they need to fully explain what a rating of 4+ actually means and how a parent can use that information responsibly. They devised the rating, so they need to let us know what it means. If they see any disinformation, they need to correct it,. If they see videos providing false information about how their parental controls work, they need to be correcting this information. Why didn't a single Apple employee reply to this thread?
I, for one, would never expect a 4+ application to get unrestricted access to the internet if I had disabled safari. Delegating the blame to the parents is just the type of socially irresponsible comment which prevents the world becoming safer for our children and lift just a little of the burden parents face bringing up the future.
So yes, we parents need to be fully aware that a child is never safe with our new technologies because despite the PR about how kid safe they are, or the great parental controls, they are meaningless unless we are fully informed...