Two things

Firstly, was your son really on the back seat as you said or on the passenger seat on your right hand side? If he's on the front seat, yes the seat bell warning light would be on, I am not sure it's the case if he seated in the back though,
Secondly you don't have to go to your dealership for a report, your car user manual should explain what the warning light does. You can just show that to them.

I would if I were you go to the court to challenge them, after all it's not a small fine, and, your insurance premium will be probably affected.