Yeah, when I first started with Ancestry, I set up a tree online and thought it was private, then later realized it wasn't, so went in and changed it. But then I still had problems with people being able to copy stories, etc. from my private tree (items I had added after I'd gone back and reset it to private).
I like the idea of being able to access my tree from my desktop computer, or my phone, etc. As well as ease of mind when my laptop dies like it did this month.