I recently ran into a situation where a private tree owner is predicted to be a fairly close relation to me, which is a fairly rare occurrence since most of my matches are distant. I wrote to the private tree owner and pointed this out only to receive a response to the effect that they reviewed my tree, didn't see anyone they recognized and weren't ready to make their tree public.
It is frustrating to deal with someone else whose own research may not be as extensive as your own only to have them tell you that they don't recognize anyone in your tree. Just because they don't recognize anyone in my tree doesn't mean that I won't recognize anyone in their tree. If their tree's lines only go back to the 1800s, they certainly might not see familiar names in my own which goes back to the 1600s but that doesn't mean that we don't have a common ancestor.
On the other hand, I have made private trees myself when I am just trying to research a particular person's ancestry and don't know as yet whether they are connected to anyone within my own family, so I can understand why people might choose to have private trees for non-DNA related reasons; still if you are going to go to the trouble and expense of DNA testing, being unwilling to share your info with your own supposed relatives seems unwarranted.
Michael