First post, and I have a theory of why hoax believers think the LM is top heavy. (NOTE: I don't believe in the hoax)
Essentially, it boils down to the LM being so wide relative to its height. After all, everyone knows that rockets are tall, thin and pointy, and since the LM is so wide, it has to have so much more weight up top, so it's top heavy. Rockets aren't top heavy because they're thin at the top.
It almost kinda sorta makes sense, if you try not to think about it from a scientific or engineering standpoint. Or more likely, if you've never encountered or heard of such exotic concepts as 'center of mass' and 'moment of inertia.'
Ironically, having the center of mass so low actually makes it not top heavy. Still, the non-engineer part in me wants to think having the mass distributed low and wide could cause problems with stability, requires excessive maneuvering, which would be engine gimbaling, if a force is applied at the side, far from the center of mass.
Of course, the answer is that the (ascent) engine is fixed, and in a vacuum, there isn't anything to apply the force. Except for the RCS system, where being so far off to the side actually makes it work better.
Also ironically, the Soviet version of the LM, the LK, apparently actually suffered from the 'moving astronaut' problem they accuse the LM of. Really, the cosmonaut's center of gravity had to stay within 3 cm?