You are right. I mentally think of it as a “starter battery” because the 12 V is needed to get the car going when the “Start” button is pressed. If that 12V is dead, the car won’t start no matter how much juice is in the hybrid battery.
The tricky thing about jump-starting a Prius is that the battery is way in the back of the car. The manual says to use a special terminal located inside the fuse box (under the hood) to jump start the car, but I could not get that to work after multiple tries. When I attached jumper cables directly to the 12V battery, however, the car started instantly. The tricky part was snapping out some of the plastic cover pieces in the rear of the car in order to get to the battery – a chore that was made even trickier because the release for the hatch is electric as well and won’t open when the 12V battery is dead! Luckily, there is a manual method for opening the hatch from the inside, although that requires climbing over the back seat and twisting yourself into a Gordian knot.