Why do you keep your dna tree private? What is the point? Would you do so if everybody's dna tree were private? I Think not because then there would be no point in dna testing at all. There is no point to dna testing if you do not want to share (assuming you are interested in the genealogical aspect). If you are worried about access to our pictures and documents, it is such a simple thing to make a barebones tree to attach to dna with only names, dates and locales so that your matches can look for a connection.
I don't contact people with private trees generally. I don't have time. They go into the trash.