You may want to check out the ancestry blog. I believe ancestry is better now than what you and I may have experienced in the past.
The issue now that I have seen yesterday is that a living person that I know, is listed in someone else's public tree and not shown as private. I have not seen this in years so I think this is a a glitch and not intentional.
I would never put highly sensitive items on ancestry or any other online location. I would keep that offline. For some items that are somewhat sensitive, I would go with a non-synced FTM tree or other desktop program.