Well, I don't have my family history records on any submitted tree on any commercial website, but if I did, I would not be including a lot of details, and I would certainly not be including anyone from a generation or two before me, as there are some rellies from those generations who are still alive, so they are entitled to their personal privacy. Perhaps I am old fashioned, but to me, family history is about researching deceased ancestors, rather than seeking out those who are currently living.
So if someone wanted to 'nick' my own research and re-label it as though it was their own, then I see no reason to make it easy for them to 'nick it' by publishing it online on any of the commercial websites.
On the other hand, if someone has nicked information about any of my own deceased direct ancestors, whether they are actually somehow connected to me through a shared ancestor or not, makes me concerned about if they are actually seeking access to my own identity, or perhaps the identity of any of my living rellies. And if they are doing that, in such a backdoor way, do I have concerns? YES, then I do.
But I cannot see that Ancestry or any of the other commercial websites, who all seem to have rules and terms and conditions about not displaying the names of the living are causing the initial issue. I would expect though that they should re-act promptly to requests about privacy of the living. I don't see what they can do about those who want to copy your research as though it is their own, or worse still the poor form where you contact your fellow members and ask for confirmation of their own independent research when you can show that that research is likely to be authored by yourself.
As tactfully as possible, may I gently mention that those who are already deceased are not offended by what is published about them after their deaths.
So, in that respect, I think our own worst enemy is not Ancestry or the commercial websites like Ancestry, but rather the popularity of our shared hobby, and the lack of publicised standards for the publication of that research on the web.
Cheers, JM (Edited to add two final paragraphs)