What appears to have happened here is that a music producer on the show found the song and thought that it was just an ‘internet musician’ that they could cop it from and no one would be the wiser. Unfortunately, Coulton is an immensely popular performer and almost universally beloved on the Internet.
Even Coulton is unsure which rules apply:
I have some questions about how IP works in terms of this song. It’s a cover of a Sir Mix-a-Lot song obviously, but I wrote a new melody for it, which this recording uses. Back when I released it, I bought the statutory license to distribute my version of this song through Harry Fox. Creative Commons doesn’t come into play because it’s a cover song, and anyway my CC license specifies Non-Commercial. A complicating factor is that, to my ears, it sounds like it actually uses the audio from my recording – not the vocals obviously, but the instruments sound EXTREMELY similar.