This came into my mind too. Great song, and yes, better than the already-good original.
Struck me as a strange choice of cover.... original fairly recent and in the same genre as the Pixies. People normally jump back in time or across genres for covers. They didn't attempt to significantly re-imagine it or anything either, but still worked.
Hadn't seen the video before..... very good! Quick Wikipedia search shows that Black Francis only agreed to make a video if it was shot in one take of a live performance/mime by the band.
The director had the idea to set up 12 cameras focus on top/middle/bottom of the 4 members, cut into the 4*3 grid in the video.