That approach supposes you have copies with some date stamp that were provided to an outside source. I've got some part written stories that are over 10 years old and unfinished, never been seen by anyone else. The fact they only exist on my computer with some sort of computer added date stamp is not sufficient legal evidence because that date can be easily altered by me to read anything I like. Like many authors I don't send a copy out for editing until after the story is completed.
That's why, for hundreds of years, authors would routinely mail a copy of their initial manuscript to themselves, never to open it, so that, if contested, they could prove the story idea was indeed, theirs alone.
It's hardly a new problem, and emailing a chapter or two to yourself is much easier than mailing an entire manuscript across the country. The point is, there are ways to cover your ass. If you don't, then you only have yourself to blame.
In fact, many sites, such as Bowker, have a facility to record your entire document, so they can, if the need ever arises, do a literary comparison between document to determine whether someone is ripping you off. (I've never used it, since my stories are rarely ever 'finished', but still, the facilities still exist.)