Actually, no. There is no contract if there is no meeting of the minds. They intentionally withheld relevant information about the "delivery", so there was no meeting of the minds and thus no contract. There is a huge difference between delivering a package/pallet/whatever ten miles in a half hour and driving ten miles in a parade in several hours. Even if you ignore the moral dimension of the message they wanted him to convey, from a business perspective he was lied to. I have also walked out on agreements when I found that the other party was misrepresenting the situation, and I am in complete agreement with his response as a business decision. I do not deal with those who lie to me.
I suspect that somebody in the company wanted to have an excuse to fire the driver, and knew just that would set him off.
Those libs posting at the article, complaining "he violated his contract" would probably sing a different tune if it were a case of a gay driver being told to drive a sound truck for the Westboro Baptist Church, or a feminist being told to drive a pro-life sign truck.