What kind of P-bass is being used in this video?

http://www.4ad.com/breeders/video/safari-file-0/

This is the video for the Breeders song "Safari", Josephine Wiggs appears to be playing a '51-style precision but instead of the standard '51 single coil p pickup it has a big humbucker at the neck. Is this some different Fender model, or do you think it's a knock-off or a regular '51 that's been modified?

 

Cool, thanks.