Parodies aren't considered infringement. Weird Al most likely gets permission anyway. Copyright registration doesn't guarantee anything, just that there is a filing of the song on a specific date that you can use in a case. Anyone can sue anyone for anything. Unregistered copyrights are still copyrights, you can still loose if you're up against an unregistered copyright. It's only one layer of protection, not a cure-all. There are 2 copyrights, the author and the publisher. Copyright is guaranteed by the Constitution and is no longer dependent on making your claim by filing.
Disclaimer: I am not a laywer and nothing in this post is considered legal advice.
