This is an age old question and what the Ask the Counterpro program was started for to help counterpeople become better at what they do.
In one of these cases where customer are wrong, well you just have to eat the crow. However, most of our systems are capable of including the VIN code on them. Also, it is not out of reason to ask the customer what the made on date in the door jamb says.
Customers are not always right but they are always the customer.
However, this customer may be scamming you in some way so watch this one closely.