The reason H2O on Earth’s Moon would be underground is that surface water would boil off in the vacuum & low gravity, ice would sublime, etc. But conditions a few feet down are much different. By your reasoning, the well @ my home must be dry — luckily, conditions 50 ft. down differ from the surface.
As for oxygen, there is lots of oxygen on & in the Moon. Just not in breathable form. It is in the rocks. Look it up.
I agree about the green men and cheese, however. ;-)
You still did not answer my question: If many moons have from some to huge qty’s of H2O in them, why would Earth’s moon not have at least some?
I don’t think there is ice on the moon but if there was, I don’t care.