What you say is true, however all of those cheap basses he plays do not sound like the CS.
To my ears, that Nate Mendel P-bass of his sounds horrible. It's actually what convinced me that sound is not just in the fingers. Ugh, that bass.
Still, my MIJ 60s P with flats does a convincing Pino. I sure don't.
It's the Seymour Duncan pickups. They are polarizing, I know what you are saying.
My classic 50s sounds a lot better and holds it own against my AVRI63, which is very similar in tone to his custom shop (maybe same pickup?).