I've had to file takedown notices for my published work. I found it on pirate sites, and did get it taken down. It's the stuff I'm publishing online, for free. I mean, really... just read it, and if you're needing to download it to read offline, just tell me. I'm pretty approachable, I think, and more than likely, I won't have an issue with it. It's the surreptitious stuff that bugs me.
We do indeed have a timestamp of when a story was first published with us, and provided you haven't taken it down and reposted it, that date will be there forever. FFN does the same thing, and so does AO3. Any reputable site will do so, I find.