Besides the poll data to refute this statement, I want to point out:
- there is no 1 Fender Precision sound. Over the years, there have been so many different Fender Precisions - even if you limit it to split coil, passive basses - that there is no way you can say there is just one P sound. Different body woods. Different fret board woods. Different ways of making the pickup. Different tone caps. Different whole tone circuits.
- Just because you can hear a difference between 1 particular P bass and 1 particular PJ does not mean (AT ALL) that the difference is coming from having the J pickup. Two "identical" basses - same woods, same strings, same pickups, same everything - will often sound different.
I'd be willing to bet money that, if you took 100 different randomly selected passive Fender Precision basses, where 90 of them were P only and 10 of them were PJ, NOBODY could reliably pick out the PJ basses. They may sound slightly different, but ALL the basses in that batch of 100 will sound slightly different.
So, fretting (heh heh) over whether having/adding a J pickup will make your P bass not sound like a P bass is, as my dad would say, just mental masturbation.