OK, let me repeat. You haven't been here for very long so it probably hasn't come up. I'm not offering evidence today, in this particular case, but I make my living as a scientist -- I do brain research for a living and hang out here from time to time because I like the forum and most of the people. Including you.
Now back to the issue at hand. There is plenty of empirical, scientific evidence that the conditions as described create a condition of uncontrollable stress for the animal. His physiological response can reasonably be interpreted as evidence of that. Not the fact that he had to excrete but the nature of the excrement. Please, I don't want to go into further detail on that, but it has been well documented in the scientific literature as evidence of severe stress. To be strapped to the top of a moving car (carrier notwithstanding) for 12 hours would be extremely stressful. I'll bet if someone had taken the dog's cort levels at the end of that trip they'd have gone off the charts! It would be interesting to know how he behaved after that ride and if they returned home in the same manner.
It isn't even recommended to crate dogs for more than a couple of hours during the day in their own homes, never mind on top of a car! Today, they most likely would put him in a kennel for the duration of their vacation and collect him when they returned.