If errors in a tree was grounds for keeping a tree private then most trees should be private. At least any tree that goes back more than a few generations. It's through sharing and comparing that many of these errors come to light. I recently compared myself to a DNA match in which we had the same individual in our trees and looking at her tree, I realized the marriage data differed. She had the first child born which I did not, and the marriage date in my tree was several years after the first child was born! I researched the discrepancy and found the official register which showed her date was correct.
Nevertheless, this appears to be an unwinnable argument. All I know is I have 4500+ matches, and a pretty sizable number are private or no tree. Sending a message to each and every one is not practical. The only decision I have is to remain public or go private so I get to be the one who holds the cards. Heaven knows I got some errors...!
What if everyone was private?