I'm more into just educating the users to not post shit they don't want out in the public in the first place. No matter how good the efforts of the server administrators are in removing the content, there's still the possibility of users, be it actual humans or bots, collecting that content and continuing to spread it elsewhere or otherwise use it.
I mean, go ahead and follow their request if they do ask, but also explain to them to maybe think a little harder about what they are posting because you cannot guarantee someone outside your sphere of influence doesn't have the same content saved somewhere.