I've spent many years dealing with customer service issues owning an IT company for years. The customer is the reason you have a job. If customers have questions, they deserve to be answered correctly. This service manager blew you off and gave you the answer you wanted to hear. Only when you came back with information that proved them wrong is when they finally admitted the mistake.
The IT world and auto service industry share a similar dynamic, the customer doesn't always fully understand what you are doing for them (but some customers do). It seems like you gave them enough rope to hang themselves and they did. I would move on to another dealer who will appreciate your business.
My $.02
