I wouldn't call the Moon "well within" the Earth's atmosphere.
The atoms there that source from Earth's atmosphere are incredibly thin, what we would call a vacuum for all practical purposes. But it's enough that it's detectable with scientific instruments, which is interesting and relevant for space exploration and studying other planets, to know that traces of atmosphere are detectable that far away from the host planet.
By analogy it would be like calling Earth's night side "well within" the illumination from the bright star Sirius, because its light is detectable here, but we sure wouldn't think of it the same way as the day side of Earth is "well within" the warmth and illumination of our Sun.
From the article:
The new study revealed that sunlight compresses hydrogen atoms in the geocorona on Earth’s dayside, and also produces a region of enhanced density on the night side. The denser dayside region of hydrogen is still rather sparse, with just 70 atoms per cubic centimeter at 60 000 kilometers above Earth’s surface, and about 0.2 atoms at the Moon’s distance.
“On Earth we would call it vacuum, so this extra source of hydrogen is not significant enough to facilitate space exploration,” says Igor.