To me this looks like a blatant attempt at a cover up to hide a critical mistake they made... like their inability to admit fault is going to make them liable for something.
That statement is closer to the truth than you realize. When lawyers are involved they will tell you never say anything and never admit a thing. If someone (like you) are going to make claims or accusations the lawyer will say make them prove their case, do not make their case for them.
We would all like to believe it would be just easier if they admitted they made a mistake and then moved forward and be done with it. Well that is all fine and good if there were not a few people out there who are more than willing to hold people liable for everything they did even if they were not wrong. We live in a country which is sue happy which makes it hard for the rest of us to get what you would deem a simple thing to resolve.
Also, the fact you posts the dealer's name all over this board and threaten them with dragging their name through the mud basically sealed your case with them. They will not help you at this point and if they do with a help of a lawyer you most likely be required to getting your statement pulled from a public forum. There is no such thing as freedom of speech when you trying to get a company to do something for you. You can fall on your sword here and you will be right but it does not guarranty they will fix your car without you spending lots of money on a lawyer and the Dealer know this.
You mistakenly think you have some sort of power of leverage over the dealer, you do not yes you can drag their name through the mud, but they can turn around and make you retract everything you said if you not willing to take it to court and prove your case.
Basically the ball is on your court and you will need to make this all go away before they will help you without brings lawyers into the middle of it.