If the dealer lied, you SHOULD post their name. **** ’em. And the answer to “I’ll speak to my manager” is simple … “If you can’t make a decision on price, then bring out the manager who can or I’m leaving in five.”
Also, if you’re arguing about $600, you might not want a new car all that much. Get a decent used car for $4000-5000, stick it on a 2-yr promo card for a low rate, and be done with it.