check engine light caused by loose gas cap

I just bought a 2015 smart fortwo pure used. It last had its service B done in July 2017 at 16k miles, so even though it's only at 23.5k miles I decided to take it to dealer straight away for an oil change (the check engine light was on). The guy at the dealership said it would cost $175 to diagnose the check engine light in addition to the servicing fee. This morning he got back to me saying the check engine light was because the fuel cap is loose. The thing is, I only stopped for gas once between when I bought the car and when I took it to the dealer, and I'm 100% sure the cap was tight. I specifically got out of the car to remove and put the cap back because I didn't hear the clicking sound when the attendant closed it after he was done. My question is, is it possible they made a mistake in diagnosing why the check engine light was on? Is there anything else I should ask them to check?