That NG article has a definite fearmongering tone. However, the correctness of the calculation should be considered very separately from the question of whether such a tiny shift in the axis by a few centimeters would matter in any way, shape or form.
The distance from pole to equator is ~1E7 m, and ten centimeters are 0.000001% of that, so it's not that inconceivable to me when comparing to your number of 0.001% of the earth mass.
