Hey Alex,
Yes, its possible to sell cars with Facebook. The answer to the question they asked you is yes they all MUST be on Facebook for these reasons:
Customer Support : A lot of people start to search on Facebook before Google if your dealer is not there another one could get the lead. If a customer want to interact with you he want to do it in public since he have the ''community protection'' companies cannot risk saying bullsh*t with social media today.
Brand Management: People are talking about you or your local brand. You must be there to keep track of this with the community.
Awareness: A lot of your competitors are on Facebook and this year will be one of the biggest year in the history of Facebook with dealer subscription. You must take the wave now.
A lot of dealers post hot deals, incentives and price cuts with very low results on Facebook. Its not a website for selling... use marketplace is you want to sell directly on Facebook. Otherwise its not the place to do that.
Use Facebook for only 1 reason : Build Trust!
Build your facebook profile in order to get the community trust. Nothing fancy or fantastic, people just want a trustworthy dealership friend. They will contact you if they are looking for a car. Trustworthy dealers seems to be more rare and valuable than a diamond of 1 pound.
How can you build that?
First, you gotta stop thinking about making money and start thinking about making good relationships.
Second, you must make your ''tribe'' feel good emotions by following you. Make them laugh with funny pictures or videos, make them feel proud about being american, make them feel smarter with hints and tips to save money with their car, make them feel good with contests for a local cause, make them feel trust with real testimonies from local buyers.
Third, be constant with your post. Be at least on Facebook 1 time per day (5 minutes is enough). Make a daily presence at least with a like or a status update.