The Earth's gravity well extends far beyond the atmosphere. The moon is for example is well inside the gravity well and even the hill sphere meaning Earth's gravity is the dominant gravity force on the moon.
Right, but gravity well isn't the boundary where outer space begins. The moon is clearly in outer space, so I'm not really sure why you'd suggest that "within the gravity well" would be inner space.
In fact, Earth's gravity well never ends, it simply diminishes with the square of distance. The entire universe is within Earth's gravity well, so where would you even put the boundary? Where Earth is no longer the largest gravitational force?
Anyways, it doesn't matter because as you clearly demonstrated, it can't be related to gravity.