First of all, a celestial body could appear blue for a simple reason: it may be blue, indeed. This is the case of Neptune. Its being blue simply means that the probability that a photon is reflected off Neptune is higher if the frequency (color) of the photon is basically blue than when it is green, yellow, or red.
However, the Moon isn't actually blue. The percentage of the photons of different colors is basically the same in the sunlight and the moonlight. The fact that we think that the moonlight is bluish is an optical illusion known as the Purkyně effect after a Czech 19th century biologist.
The reason of the illusion is rather simple and you sketched it. The human eyes depends on cones and rods to see. Cones are able to distinguish colors – basically, they give us the detailed colorful information about the amount of red, green, blue (like the RGB information about colors on computer displays).
Cones are most sensitive to the green-yellow light in the middle of the visible spectrum. The most neutral color of light is "white" but the light from the Sun is a bit separated. The blue, high-frequency component, changes the direction a lot (scatters) which is why the sky is blue, while the remaining light arrives from the direction of the Sun. The "opposite" color to blue is basically yellow which is why the Sun appears a bit more yellow, not quite white.
Cones with this RGB color sensitivity could be enough to see everything in color but they have one disadvantage: their sensitivity is worse. That's why the eyes also have rods. They can't distinguish colors but they can see even dimmer light. Their sensitivity just happens to be maximized for colors that are blue-green or something like that.
So when thc ones already "see nothing" because the light is too dim (weak), the eye relies on the rods. The eye effectively becomes color-blind but the brain must still interpret the colors in some way. It interprets them as the color that is normally maximally correlated with the rods' seeing something, i.e. with the frequency at which the rods are most sensitive. And this mechanism gives our perception the bluish color. It's because the eye starts to rely on different cells which are maximally sensitive to slightly different wavelengths (colors) than the average cones.