Disclaimer; this is an argument based entirely on logic rather than anything in the RAW.

The moon is the lightsource on a moonlit night. Creatures with LLV treat a light-source as having twice the radius of bright illumination and twice the radius of shadowy illumination.

If the world itself is in the moon's radius of shadowy illumination for creatures without lowlight vision but in the bright illumination radius for creatures with LLV there's no conflict.

Creatures with LLV can see in the shadowy illumination of a moonlit night because the light-source's doubled bright illumination radius includes the whole surface-world.