Why don't you put up a stripped version of your tree?
It's not a matter of ingnoring the Private Tree. I have contacted many private trees only to be ignored. I have also seen where they have no problem plucking from my tree and don't have the courtesy to share with me. It would be nice if I could block those people.
As far as the "No Tree" people I have found they usually have multiple trees. Most have their parents trees split so they don't attach. I always look at those.
Adoptions can be a sticky situation. I too have that in my tree. We know who the bioloical parents are so that tree is private and we have no plans to run a DNA for it.
It goes both ways.... loss for those of us who are tired of contacting "Private Trees" and a loss for the "Private Tree People" who might find out information after contact that is not in the tree.