They would get it wrong, though. Even the physics 101 students probably wouldn't draw the gravity of the sun, the gravity of the earth and the Milky Way.
If we're discussing reasoning from first principles, is it really so intuitive to disregard the gravity of the Earth in this experiment? Why can you disregard it and still get the correct result?
Exactly right: you have to recognize that the moon is in orbit/freefall with respect to Earth, which means there is no gravitation near its center of mass and only tidal forces away from the center of mass. Then you have to estimate that the tidal forces on the astronaut will be small compared to the moon's gravitational forces on him. None of this even counts centrifugal forces from the moon's rotation or effects of the sun. Nested non-intertial reference frames play merry hell with the simplicity of a FBD sans prior knowledge (or solid logical reasoning) about what can be neglected.
Even with a physics degree, my kneejerk reaction didn't come from first principles. I, too, was doing "stupid pattern matching" -- the only initial difference between me and the floating-pen-people was that I happened to know that gravitational acceleration could be reasonably approximated as constant on large astronomical bodies (moon is g/6). It took a few seconds for the "otherwise the planetary body would disintegrate" argument to occur to me and even longer for the formal mathematical picture.
If we're discussing reasoning from first principles, is it really so intuitive to disregard the gravity of the Earth in this experiment? Why can you disregard it and still get the correct result?