Wasn't the copyright office the ones who had Win XP computers in 2015?
I think the text is a little biased towards registering.
The is such a thing as a webcrawler at archive.org, which in fact "crawls" the websites of the world and archive them. This means that you can validate old material that has been uploaded on the web, because archive.org is an independent organization.
For copyrights this means that you can find evidence of your copyright from the time where archive.org registered the content on the website.
Because this evidence is collected by an independent organization, you can use this in a court of law.
A court of law will evaluate the collected evidence as a whole, so every little bit counts. And evidence collected by an independent organization, which you cannot manipulate, is hard proof.
So, for the question it implies that your song is basically "published", in the sense made publically available, when you upload it to the Internet. Anywhere on the Internet, where the general public (and webcrawlers) has access.