I asked a private tree DNA match if they'd share their tree with me, but they elected not to. Told me they don't invite anyone who is greater than a 3rd cousin match. Person claimed we have no match.
I have brick walls at that point, where I can't go beyond great great grandparents. We could have a match, and it could be at the 3rd or 4th cousin level.
I tend to think Private Tree owners don't see all the possibilities....