Back when I was a kid, very little property was actually posted, but I was raised to understand that I should have permission before entering someone's private property ..... posted or not. In fact I'll bet even the city kids knew better than cutting across their neighbor's yards even when that would have been much more convenient. We were taught not to assume that I had some kind of right to use other people's property. I guess in this day of permissivness and coddling, that little item of respect has been omitted for some and apparently with the blessings of others. No, there is no excuse for arbitrarily entering someone else's property without permission .... especially (but not exclusively) when it is posted. And that applies whether the trespasser is a kid, adult, or whatever.
As far as getting kids involved in the outdoors, I would suggest that the first lesson to be taught to these kids regarding outdoor activities is to respect landowner's property rights. They don't learn that by us making excuses for them to break trespass laws. I know it is fashionable to excuse everything that kids do these days, but that doesn't make it right.