HOLY mother of pearl!!!!!!!!
He's definitely going for that saturated sound (I like that too!), but they can be less "fuzzy" if you want them to be.
Here's a couple home recordings I've done with EBs, both with sounds that are fairly unprocessed, straight up mudbucker sound.
This is a '68/69 EB-0 with mute on and tone at about 50%:
This is a '66 EB-2DC in all its muddy splendor. Theres a bass solo thing in the middle where you can hear it up close, dubious bar bridge intonation and all
I used those basses in band that did heavier rock stuff, and I would tend to crank the preamp for some overdrive (like the video clips above) would get the bass to cut more in the mix of things. Borrowed that from these fellers' sounds