If the local government does not mail you the bill, then yes, that would be it. We have that happened too. But I have yet seen a US rental car company not to charge the Admin fee.
The mechanism works this way - government sends the car owner the fine. In this case the car owner is the rental car company which then spends time to identify who rented the car in the period that the fine occurred. Then it informs the local government the offender's information (name and address). The local government in turn sends the offender, you, the bill of the fine.
As for how to handle it, I agree with both Helvetia and 雲燕假日
