Wiring P-bass "63

Besides the different cap. values in the two, the Seymour Duncan's plan doesn't explicitly carry the ground from the pickup signal all the way through to the output jack. It depends on some other means, e.g. shielding on the underside of the pick guard to do that. If that isn't a connection, then the output is the difference between the hot signal of the volume pot output and the hot signal through the tone control.

If you'd connected both pot bodies to a star ground or just connected them together, then it should've sounded the same as the Fender setup. This is assuming you used the same cap for both of your configurations.

Having two different ground paths could make a ground loop problem. If you don't have excessive hum I wouldn't worry about it. If you do have an extra hum problem, I would insulate the pots from the pickguard with plastic washers. That way there would only be one path to ground, through the pot bodies. That said, I've never taken any precaution to isolate pots from the shielding on the underside of a pickguard, and I don't seem to be suffering from it.

I have some pickups that exhibit the problem you mention, e.g. a Bassline P pickup where one pickup has that problem and the other doesn't. I'm guessing that the coil wire gets scraped or something and makes contact with the poles. If the hot end of the wire is in contact, then the touching the pole will make it buzz, otherwise it wouldn't be noticed. That's just my crackpot theory on that though.