No, that's just wrong: at no point is (say) a Toyota Hybrid burning gas to generate electricity to immediately turn another motor that actually moves the wheels.
There's a video linked elsewhere in this thread that explains how the toyota system works, it's worth watching as it clears up several common misconceptions about the system.
... and instead drive one of the motors, generating electricity to power the other motor to push the car forward.
I feel like that video you're mentioning did a poor job if it didn't describe one of the more important and clever aspects of the Prius's design.