No DL with an electric helper motor is how the state law reads to me.
Gas helper motor needs a dl.
Here is what I think happened.
The movie " who killed the electric car " kinda explains the former Calif electric car laws.
Dealers in Calif had to sell a # of electric powered cars.
Electric bikes were not legal at the time so laws were changed so they would be legal and dealers could sell them to help comply with the law about # of electric car sales.
A new Fed law was passed and many states also followed with new electric bicycle laws.
This is where the electric bicycle laws came from.
The electric car didn't die but went on hold and the electric bicycle and the electric bicycle laws live on.