0.012 inches (or approximately 0.305 mm) is actually fairly sturdy, under the right circumstances. See this related answer as well, but a soda can may have a wall thickness of 0.1 mm or even less and is capable of containing 30 pounds per square inch (psi) against a standard atmosphere's 14.7 psi pressure on the outside (a 15.3 psi positive pressure). (The ICAO definition of a standard ground-level atmosphere according to Wikipedia is 1013.25 hPa = 101325 Pa, which Google converts to just under 14.7 psi.) The LM was not tasked with such a pressure difference: according to Apollo Expeditions to the Moon, chapter 4.4 and Apollo Oxygen And Two-Gas Environment Problems, Apollo missions used a cabin pressure of approximately 4.8-5.0 psi in flight. (NASA states "5 psi" on the former page linked whereas the latter page linked states a more exact "4.8 psi"; whether it is more accurate, I don't know, but the difference between the two numbers is small enough to be insignificant for our purposes.)
Under a positive pressure, materials tend to expand. Provided that the strength of the material is adequate to hold in the positive pressure (if it wasn't, the LM would have ruptured violently most likely during ascent tucked away inside the Saturn V as the pressure difference between its interior and exterior grew), this also tends to make them rigid. As even a thought experiment, take an unopened soda can and deliberately try to puncture it. You may succeed in puncturing the can, but it's likely to take a fair amount of deliberate effort. The ratio of positive pressure inside the soda can to the thickness of its wall (about 15 psi to 0.1 mm, or 150 psi per mm of thickness) is significantly higher compared to that seen by the LM pressure vessel while in flight in space, which is the only thing it was designed to do (about 5 psi to 0.3 mm, or 15 psi per mm of thickness).
So while 0.3 mm might sound very thin, and at the face of it sound like it is at risk of being punctured, by the time you consider what it really needed to do and what conditions it faced, it turns out that it most likely was quite adequate for the job. Going with thinner materials also saved a lot of weight, which made quite a big difference in the difficulty in going to the Moon at all. If the people designing and building the LM had used something "obviously sturdy enough", it's entirely possible that there would have been no need for the LM at all because the tyranny of the rocket equation might have meant the additional mass made just the difference that killed the idea of the Trans-Lunar Injection (or even earlier). It certainly would have required the Saturn V to be even larger than it already was, to get the additional mass into a transfer orbit to the Moon.
And of course, if the hole was small enough, you could just patch it up. Even a "simple" space suit can handle a puncture. Only in movies do things violently blow up or decompress because of a small hole. Heck, people have survived being exposed to very low air pressure, including during Apollo equipment testing as well.