There is enough information online to identify people, especially if they have anything unusual about their names. It's not long ago that I shocked fellow trustees of a charity I was a trustee for, by handing two of them (both married and female) a piece of paper which their mother's maiden name and at least one past address was written on. All I had needed was their everyday names and a good idea where they lived.
Any competent genealogist in the UK can fill in the boxes on Ancestry marked "private", unless there's a common surname involved. For that reason neither my daughter nor her children are included in my tree, which is also private.