The whole myth that a P bass with flats is the most authentic usually reflects a lack of trying new things. I respect Juan, but a P bass has nothin' on a semi-hollow piezo fretless strung with some nylon flats. The piezo and P may have similar tones, but the piezo picks up much more finger noise and percussion, which can be vital for faking an upright tone.
Juan doesnt play just a regular P to get an upright sound. He plays the really old fretless P's that were only around for a few years. I have a self modded fretless P and it doesnt he job for an upright tone. It still has a very warm sound without the brightness of a fretless Jazz. But I really dig the clip of the Rob Allen Mouse 30 . Sounds really close to an upright. Just get out and play alot of different basses to find the one you think sounds good.

...You'll be IMPRESSED.