If he bothered to look there are plenty of pictures of the actual hull without the insulation. It's construction is quite elegant.
And robust, despite the descriptions of its thin skin. If you go to Kansas you can see a lunar module without its clothes on. The chem-milling techniques used to make the integrated skins and stringers were considered fairly advanced back in the 1960s.
The descent stage structure is made from four aluminum panels built like beams, with appropriate stiffeners, arranged as a tic-tac-toe board. Everything is bolted to one of those panels. The skin -- blankets of the aforementioned films laid up in thicknesses of 20 or so layers -- is simply wrapped around it and only has to support its own mass. The landing legs attach to the ends of the beam panels, such that when it's sitting on the lunar surface there is a pair of beams spanning each pair of two diametrically opposite legs. The legs are tubular aluminum, the same method used to construct secondary structures of airframes.
This is the same method we use today to build spacecraft chassis. More often than not a spacecraft chassis is an interlocked or interleaved set of bulkheads made from honeycomb plate or similar high-strength, low-mass materials. The exact arrangement depends on mission requirements for structural stiffness and strength. But if you were to remove the insulation blankets from a modern spacecraft chassis and the Apollo lunar module, you would clearly see the design lineage.
The ascent stage structure is a cylinder laying on its side. The fore and aft bulkheads are milled from solid plates of aluminum, several inches thick. The forward bulkhead is actually the passage from the overhead hatch and ascent engine area into the cockpit, which is secondary structure. The rear bulkhead also mounts the aft equipment panels. This method of bulkhead milling is the same as, for example, the structure around an airliner's pressure doors. By milling away all the material except for the load paths, you get a structure that's as strong as several inches worth of aluminum plating without the weight.
At about knee level, to either side, are two robust ventral beams made from aluminum sheets, the same technique used to make airliner wing and keel spars. These connect the foreward and aft bulkheads.
Overhead is the docking hatch and associated structure, which is a thick aluminum tube welded and gussetted to another milled bulkhead. This completes the connection between the two bulkheads and transfers docked maneuvering loads. This produces a very robust structure, stronger even than portions of some airliners.
Secondary structure is built out in the front to form the cockpit and to each side to mount the ascent propellant tanks. Standard aerospace-type beams are used, as well as aluminum tubing struts.
The pressure hull is the most talked about feature. Visually it resembles standard skin-and-stringer construction that you would see in any airplane built from the 1930s to the 1990s. The same skin-stiffening methods were used in the Saturn V body and similar to SpaceX's Falcon 9 (the stringers are on the inside). Except in Grumman's case, the stringers were not attached to the skin but instead milled together with the skin to the precise shape required for each body panel. These were then welded to the secondary structure to form what was essentially an aluminum balloon. The skin portion of the pressure vessel was about the same thickness as two or three aluminum pie plates, which gives rise to the famous and true claim that you could poke a hole in it with a well-placed stab of a screwdriver. But its primary role was only to contain air pressure. It had a structural role only in partially stiffening the secondary structures such as the cockpit walls.
On the interior were a variety of composite interior panels that prevented anything on the inside of the cabin or cockpit from contacting or damaging the skin.
The exterior panels of the ascent stage were sheet aluminum (roughly the same thickness as HVAC ducting) over insulation and micrometeoroid shield blankets. These blankets employed the same hard-soft layer alternation that would be used in the M-1 Abrams tank's laminated armor.
Much has been made of the use of tape in attaching the blankets and various other elements of the LM. This is entirely proper. Tape works much better in many cases than piercing fasteners for attaching films and sheets. And this isn't "masking tape" as so many ignorant critics have supposed. This is industrial tape with pressure-sensitive adhesives that are stronger than bonds achieved by many off-the-shelf glues. I can literally take this tape (which uses Mylar as its substrate), attached a piece to an overhead beam in a building, and literally hang my full weight from no more than half a square inch of bonding area.
In more common aerospace, "speed tape" would be a suitable analogue. And speed tape's properties are within the experience of even the lowliest rampie. It's not magic, or exotic.
