Thinking that the LM would pass through its own exhaust is the same thing as thinking you can shoot yourself simply by firing a bullet in the same direction as you are traveling.
Well, you
could if you were facing a very strong wind. Like if you were sitting on the nose of the space shuttle during early launch.
I remember grimacing when I heard, during a live Columbia post-accident press conference, one of the mission managers claim that a piece of mere foam was much too light to possibly damage the orbiter during launch. Even engineers who should know better can suffer failures of intuition.