You'd be surprised what a background check can come up with these days. If you filed W2's for taxes, then your employment history might be available. The last thing that I would want to try to explain is why you left off an employer that you were terminated from on your application. It's grounds for immediate dismissal, and there is no chance in hell that any smart employer would give you an opportunity to discuss the situation.
Personally, I would put that you resigned from the employer. By choosing not to buy a vehicle at their dealership, you essentially told them that you were not willing to work under the conditions that they dictated, and tendered your resignation by actions made.