Yes. The driver is…
Yes. The driver is responsible for the vehicle being in roadworthy condition as well as paying the traffic laws. Your friend loans you a car. You will get the ticket for a light out or unsafe tires etc. That how it works. That's obvious when commerical drivers are required to do pre trips. They are responsable of the vehicle isn't safe or is missing equipment.
I'm wondering if the plate ticket was a way of on the site downgrading another offence. Test drives are easy to do silly things like forget to signal or speed. Different vehicle and different roads that you may normally drive. I can totally see an officer pulling someone over for one of those and only giving them a hassle about the plate. It saves the driver on insurance and may be done at times in good faith as a warning on the other offence since it may be an honest mistake. The officer also has to call in the no plate at time of stop. So it's on record. Would have to go to court to see about lesser fine or having it dropped. Not public media or the officer on the side of the road.