Alright, you got my curiosity going. So I've been trying to determine whether there actually are any DOT regulations that would apply to this setup. I found a few little nuggets in a Safety Tips document from Suburban Propane here
. It seems that vehicles carrying less than 1000 pounds total weight of propane and tanks do not require placarding. Open-bodied vehicles, like the underside of a bus, are considered to be in compliance with the isolation of cargo space from driver's compartment. If the capacity of the cylinder is less than or equal to 45 pounds then the cylinder may be transported in any orientation. Cylinders shall be fastened in position to minimize possibility of movement, tipping, and physical damage. Etc.
I couldn't come up with anything "by the book" that says this setup is wrong.. although yes it does look sketchy.