You might be thinking that because the earth spins, clocks on the equator run slower due to SR. But remember the earth is not a sphere, but an oblate spheroid. So clocks on the equator are also farther from the center of the earth and thus run faster due to GR. The two effects neatly cancel each other (not by accident). In fact that is one definition of sea level -- the point where all clocks run the same, minimum rate.
I'm not sure I understand why the slowing due to spin happens to exactly match the speedup from altitude.
The spheroidness of the Earth is, indeed, mostly due to the rotation, but that would be related to the overall material properties and rotation rate, wouldn't it? Would a blob of water and a blob of rock both converge to the same shape (water would move faster, but over billions of years, rock would get there)
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