It's a Fender.... either an old Telecaster/P Bass which has been modded or a new custom shop edition of one of these...
It looks like an early fifties Precision with an added Jazz pickup in the bridge position. The chick is kinda hawt.
I have a big crush on Aimee Mann and my wife is ok with that. She is so cool...I've got all her albums. Marshall
I would say it's possibly stock. I've seen a photo of the bassist from Tortoise playing a tele style bass with the same pickup configuration and wondered about it just as you did. Fender has been known to put out a few oddballs here and there, my Cowpoke included.