I too had the same problem with elderly relatives and consequently hid details of all living people on my public tree on Rootsweb when I submitted it many years ago. However, I later discovered that my tree had been displayed on Ancestry without my knowledge or permission, with a multitude of errors and personal details of living people on view. Apparently Ancestry took over Rootsweb, but not having an Ancestry subscription at the time, it was several years before I realised what had happened. Rootsweb gave me to option to hide the names of living relatives and prevent the tree from being downloaded, which I took up, but Ancestry copied my tree. It translated Mx (Middlesex) as Mexico, West Ham, Essex as West Hampshire, USA to give but a couple of examples and many dates entered in UK format were altered to US format until the tree became so littered with mistakes it barely resembled the original. I contacted Ancestry and asked for the tree to be removed as I no longer had control over it and was unable to correct the errors (even though my e-mail address was published) but since it had been absorbed into Ancestry's public World Connect tree, my section could not be removed. All the private details which I had been so careful to hide were visible as Ancestry's ruling allowed any data regarding people over 70 years of age to be displayed and names of living partners or other family members for whom no birth year had been entered also became visible. The tree was widely copied and I had enormous problems persuading people whom I didn't even know to remove the personal details of my mother and her sisters and cousins and names of family members' partners (some of whom had since divorced). However, the distinctive errors make it easy for me to spot other 'researchers' who have since copied my tree and pass it off as their own!!
I am happy to share my information with anyone who is genuinely connected to me, but my experience with Rootsweb means that I no longer have a public or private tree online, apart from a few direct ancestors' names on Genes Reunited.
Ancestry's rules have finally changed and trees can no longer show details of living people without the person's permission, so perhaps I might consider having a private tree online again. The vast majority of my information has been gleaned from searching primary sources at local record offices, the PRO, Colindale's newspaper resources and from wills as well as the increasingly large volume of info online, so I am reasonably sure of its accuracy, but there are some shocking trees online!! It's frightening to think that some newcomers to genealogy might believe that info is posted on the internet is all factually correct......
The drawback of not having an online tree is, of course, that the onus is on me to search out any new relatives, so I don't get many hits per year (I currently have 10 from Lost Cousins), but those I do are worthwhile as they are handpicked.