To maybe further elaborate on EMG's deal with production guitars and passive systems, you may find a battery in the passive HZ setup for several reasons. First off, the aforementioned preamp. If they have included a preamp, it needs the battery not the pickups, and does not make the pickups active. The reason you'd do this? Usually, someone buying a guitar with HZ's would like it to sound like 81's or 85's or whatever. The preamp gives you the extra volume of the full active EMG. But with it comes the fact that you also boost the passive system's noise. Still, you got that basic heavy output that the active setup would give.
Another reason for batteries with passive HZ is if there are tone circuits included with the guitar. EMG makes the EXG and SPC among other things, which act not so much as a preamp, but as a Equalization deal.
As for the guy that tried to wire his 500k pot to the EMG setup, you're correct, it will not work. 25k pots need to be installed. If you mix passive and active pickups and use the preamp on the passive side, you still need the 25k pots.
Hope this helps!