If it really came down to it, having all the time stamped stem tracks, meta-data, and modify dates on your computer must count for something, no?
I guess it's different in different countries but I'd hope there'd be some common sense used in the absence of irrefutable evidence.
If you suddenly claim ownership of a song I wrote, I'm going to have an absolute shittonne of not-quite-evidence to strongly suggest that it's mine.
There'll be email references the song in various discussions, copies of lyrics sent via email providers, cloud services, note apps, etc, handwritten copies, audio sessions, backups of audio sessions, mp3 bounces at various stages of the mixing process, royalty company registrations, online distributor registrations (depending when you steal it), records with publishers, details of communications with mastering engineers (again, depending when you steal it).
Various people would have copies - co writers, managers, mastering engineers, maybe contributing musicians, friends/family.
Traces of having sent copies to people - maybe copies on soundcloud or e-paper trails with wetransfer or dropbox, feedback threads on forums with mp3 links or uploads..
Obviously not everyone would have all of these things, but a lot of them are common and accessible.
I have no idea if this would ever be taken into account but there'd also be trends and traits in the writing that would be comparable to a wealth of previous works.
Commonly used lyrical patterns, inflections, rhyme styles, melodic styles and traits.
Now, I get that none of this is really evidence but it's a lot better than what you're going to have, right?
Maybe this is bullshit and irrelevant - I'm not pretending to know how it works..it's just what I keep telling myself.