I'm not sure if this was mentioned on the commentary, but couldn't he have gotten a set of strings for a 5-string, and just put the lowest 4 on his 4-string bass?
Possibly. But I would think using such a heavy string gauge on a 4 string would screw up the neck. I think it's more likely he just tuned down or used a 5/6 string bass
People put custom sets on 4, 5, 6 and 7 string bass guitars all the time. When you string up a 4 string with the BEAD from a 5 string you'll want to add a few pounds of counter-tension with a truss rod adjustment otherwise you run the risk of bowing the shit out of the neck, especially bass guitars that don't have fretboard wood like Rosewood or Ebony.
Once, when I was a kid, I took an acoustic guitar apart and modified the nut and the bridge so I can string it up with bass guitar strings. It worked great for about a week and then I started noticing the strings were getting harder and harder to hold down. Then one day as I was trying to play the bass line to "Money" by Pink Floyd the neck snapped off the body of guitar right in my left hand
The only thing holding the two parts together were the strings