Yes it does. Just because the recording was permitted doesn't mean that the recorder has the rights to publish or replay the recording.
Another example: owning a DVD does not mean you can then stream the DVD over Justin.tv.
The thing about rights is that infringement must be claimed by the rightsholder for any action to be taken. Once a rightsholder claims infringement then the content/stream/video must be shut down or removed, and if the site or person continues to infringe, THEN action can be taken.
This is one of the good things about the DMCA and the reason YouTube, Soundcloud and even justin.tv can continue to operate. It is also exactly what the much maligned SOPA bill is trying to change - for the worse.
btw, you should sign a petition against that bill on votizen or similar.
They climbin in yo' windows, snatching your youtubes up.