I could be mistaken but I believe that the present rules for existing dryer circuits echo the old rules. I don't believe that a bare neutral was ever allowed in any cable other than type SE. The key to your mystery may well be that it is a manufactured building. One of the big arguments against manufactured buildings was that they were not built to the same standard as site built structures. One of the ways that this worked out in practice was the use of wiring techniques that would never have passed inspection under the US NEC.
It is worth noting that in trailer chassis mounted units the three wire circuits for ranges and clothes dryers was never an accepted practice. Modular buildings that would be placed without the transport chassis were a different story all together.
250.140 Frames of Ranges and Clothes Dryers.
This section shall apply to existing branch-circuit installations only. New branch-circuit installations shall comply with 250.134 and 250.138. Frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be grounded in the manner specified by 250.134 or 250.138; or, except for mobile homes and recreational vehicles, shall be permitted to be grounded to the grounded circuit conductor if all the following conditions are met.
(1) The supply circuit is 120/240-volt, single-phase, 3-wire; or 208Y/120-volt derived from a 3-phase, 4-wire, wye-connected system.
(2) The grounded conductor is not smaller than 10 AWG copper or 8 AWG aluminum.
(3) The grounded conductor is insulated, or the grounded conductor is uninsulated and part of a Type SE service-entrance cable and the branch circuit originates at the service equipment.
(4) Grounding contacts of receptacles furnished as part of the equipment are bonded to the equipment.
"This alternating current stuff is just a fad. It is much too dangerous for general use" Thomas Alva Edison