Can a car salesman purposely fax a different VIN number to your car insurance for a lower quote to make the car sale?

The car salesman is committing fraud by faxing the wrong VIN number to your insurance company to make a sale.  Fraud is the intentional misrepresentation of a material fact made with knowledge of its falsity and with the intent to induce reliance upon which a party justifiably relies to their detriment. 

The car salesman is intentionally misrepresenting a material fact (the VIN number) to induce the reliance of your insurance company to justifiably rely on the misrepresentation to provide a lower rate.  You may also be liable for fraud since you are purchasing the car with a lower insurance premium based on the false VIN.

If you are at fault in an accident in that car and the insurance company learns of the false VIN, it will deny the claim and you will be liable for the property damage and personal injury claims of the occupants of the other vehicle.