I worked for MedReach a few years back, and whichever shift I worked, it was really busy; even working a 24, I hardly got any sleep. I worked in the field for more than 6 years, and I would parked somewhere hidden, mainly because I didn't want to be bothered by people asking me for directions or medical advice. Sleeping in the back of the rig is a good idea, but from my understanding of their new policy, no sleeping at all, period. To me, thats seems like an overkill, especially coming from a company that runs their crews the whole shift.
Personally, as a driver (and I was the one usually driving the whole shift, even on a 24 because my partners were not drivers), driving a lot does make me tired, and taking a short 20 minute nap while posting did help a lot, it kept me wide awake and alert for a few more hours until I was able to get in another nap. Considering that, I think forbidding crews from sleeping while they post is a bad idea, especially if there is only one driver and they are running back to back calls the whole shift. The only thing I don't know if they are allowed to sleep during their lunch break, since a lunch break is considered personal time to do what they please. If they are not allowed to sleep during their lunch break either, than that company is messed up.