I saw a closed thread regarding this, but needed this myself so here is my solution

Setup details

Untangle 14.01
Webfilter has Streaming Videos category blocked (which includes youtube of course)
Pass if referrer matches any Pass Sites ticked

SSL Packet Inspection enabled so webfilter gets access to full urls

This will allow Untangle Youtube channel only

Make 3 rules in Webfilter pass sites

googlevideo.com/videoplayback* (This is needed for the actual player)

*UC12SN_VMVLzfnL3IB5zfYzg* (This enables the channel)

*untanglecorp* (This enables video tab in channel page)

In my testing other videos to the side are still blocked.