Some kind of guitar/bass hybrid? Is it a guitar with bass strings or a bass with guitar strings or something else entirely?

I thought it was a bass six, no? A six string bass made famous by Fender and Danelectro (not the new age version of those erection basses with low B's and C's and all)? I could be wrong.

bass six/ full scale baritone?

'tis a bass VI to be sure:

http://www.southern.com/southern/band/PAULN/biog.html

It is a Fender VI. Also know as Bass VI. It is tuned E-A-D-G-B-E one octave lower than guitar. A truly beautiful sounding instrument.

used also by:
Placebo
The Cure
Brokeback

A google search for "fender Bass VI" should yield some info.

-David

Thanks all. I just found it weird that when listening to them all I could hear were two guitars and a bass, so I assumed it was something they'd built themselves that sounded more like guitar than bass.