How do you do it? and what programs can you use?

Every now and then I stumble across a website with a background song, or one of those media player bars where you can select a song. Is there a way to record a song from such a source?

I was thinking perhaps you could find a URL for the actual song file, then use a program to play the file located at the URL (Winamp can do that) and then a program could record it in to an MP3. But Tunebite can't seem to record from a URL and it needs to work through WMP, and I can't for the life of me (because I know nothing about HTML) find the URL of a song on a webpage's background or on a media player bar.

A good example of what I'm talking about is this site:
www.thedistillers.com

It's a band's website and at the bottom, they have this audio nav bar where you can play and forward or rewind through a list of songs.

Let me know what you think