All these websites (& probably a ton of trojan-filled apps that claim to do the same) "download YouTube videos" but completely thrown by pointing them at a streamed feed (after the fact, it is just a video at that point).
Meanwhile, just tell bog standard VLC the YouTube url and it'll offer a valid link to a h.264/AAC single part video file on the googlevideo domain (from which I can extract the audio, so I get my livestreamed podcast asap).
@noiob I thought the RIAA recently nuked it, but apparently the EFF came in and saved it.
Right now, I'm happy to use VLC as my FOSS route.