If it were me, I would walk. I am complicated in so many ways, but when it comes to honesty I am real basic; don't lie to me. You can tell me anything and I can accept it. If I find out I was lied to, I will never trust you, and will always question anything you say.
If I had to rely on a dealer for service and or warranty work and our initial relationship started out like yours has, I would always assume that they were lying to me and that would put so much stress on me. That stress would not be worth a $500 gift card. Also, I would always be worried that at some point, they are going to try and recover the $500 that they gave me before.
You do as you will, but I would be making some calls until I find a dealer that tells me something that materializes. Good luck to you!!