Even if the GPS receiver does not calculate speed using doppler shift, as stated in Mi5's comment, the answer is still incorrect. The answer given doesn't consider the difference between absolute and relative error. If the absolute position error is consistently off in the same direction to roughly the same extent, the absolute error cancels out when taking a relative measurement such as speed. This point was even mentioned in the original question. As a result, it is possible for GPS to return accurate speed measurements using relatively inaccurate position measurements.
Incorrect Answer
Even if the GPS receiver does not calculate speed using doppler shift, as stated in Mi5's comment, the answer is still incorrect. The answer given doesn't consider the difference between absolute and relative error. If the absolute position error is consistently off in the same direction to roughly the same extent, the absolute error cancels out when taking a relative measurement such as speed. This point was even mentioned in the original question. As a result, it is possible for GPS to return accurate speed measurements using relatively inaccurate position measurements.