it's a common misunderstanding that some have.... True "active pickups" were originally pioneered in the early 70's by the likes of Rick Turner and Ron Wickersham of Alembic, and later Rob Turner (not sure if they're related, but they're all from Santa Rose, CA) founded EMG in 1974, those companies all operated the same time and same place, so their technologies were surely similar in many ways. Alembic focused more on the "on board" electronics and pre-amp to get certain tones, and the use of low pass filters, whereas EMG was more focused on pickups with basic "Bass/Treble" controls... Active electronics were a part of what made these electromagnetically induced pickups work... without power, they were non-magnetic and so useless.
Fender and others (Sadowsky) use pre-amps inside the bass to amplify and tone shape passive pickups.. This is a less responsive but more classic sounding setup. It's why my Alembic and Spector sound so much different from my Fender, even with it's new pre-amp and JB pickups.
Read more here:
Active Pickups: All you want to know | Active Guitar