In order to get precipitation, the RH does not actually need to be 100% near the surface. For example, earlier today when the rain began, our RH was 75% in Wilmington. Now, it has creeped up to 90%.
What happens is often times the layers of air above the ground will have higher RH near 100% and become saturated to create rain or snow. That rain or snow falls into the surface air with some evaporation which tends to raise the humidity of the lower air as well, "saturating" the ground level air.
I didn't see the observation with flurries at the South Pole, but in general it is a very dry place. With low RH, a lot of the precip (snow) generally evaporates before hitting the ground, but some probably was squeeking through.
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