I was also very confused the first time a drove across without the toll collectors. It felt like I was doing something wrong, and was going to end getting a ticket.
Do you know if the person you borrowed the car from got a bill? I'm curious if they are only able to bill California plates, or they have a national database of license plates.
At least the Port Mann Bridge in Vancouver, which uses the same license plate camera only style billing, has a database which they use to send a bill to your insurance.