The trouble is that you can register it all you want and never be able to prove that you wrote a song.
In the highly improbable event that a song I wrote was stolen by Andrew Eldritch, for example, he would undoubtedly re-record the material in order to pass it off as his own. With my instrumental style replaced with Doctor Avalanche and some suitably obsidian sounding keyboards and synths on the new recording, it would very likely sound like his work rather than mine.
Even though I've registered my song on the 9th September 2008, the jury could be forgiven for being convinced that the hugely popular and critically acclaimed Eldritch with a string of hits behind him over an illustrious career spanning the last thirty years was the victim of a bizarre publicity stunt that I was trying to pull when it was taken into account that I am creating what to very few people other than me is wonderful music using a cobbled together studio built into a rather insalubrious room in my council flat where people can drink in the heady ambience of computer spares and sundry mixing equipment that my girlfriend finds about as attractive as syphilis.
In short, a jury will look at the evidence available and judge on what seems probable. Sure, I can provide demos, drafts, handwritten notes, witnesses, my girlfriend whom I wrote the song about. I'm pretty sure anyone could cobble a paper trail like that together if they put their mind to it. The trials can get very complicated as this extract from a wiki article will demonstrate:
http://en.wikipedia.org/wiki/George_Harrison
"Harrison was later sued for copyright infringement over the single "My Sweet Lord" because of its similarity to the 1963 Chiffons single "He's So Fine", owned by Bright Tunes. Harrison denied deliberately stealing the song, but he lost the resulting court case in 1976 as the judge accepted that Harrison had "subconsciously" plagiarised "He's So Fine". When considering liable earnings, "My Sweet Lord"'s contribution to the sales of All Things Must Pass and The Best of George Harrison were taken into account, and the judge decided a figure of $1,599,987 was owed to Bright Tunes.[94]
The dispute over damages became complicated when Harrison's manager Allen Klein changed sides by buying Bright Tunes and then continuing the suit against Harrison. In 1981, a district judge decided that Klein had acted improperly, and it was agreed that Harrison should pay Klein $587,000, the amount Klein had paid for Bright Tunes - so he would gain nothing from the deal, and that Harrison would take over ownership of Bright Tunes, making him the owner of the rights to both "My Sweet Lord" and "He's So Fine" and thus ending the copyright infringement claim. Though the dispute dragged on into the 1990s, the district judge's decision was upheld.[94][95]"