Not always the situation. The staff at the CLE NWS don't even measure the snow. They use an FAA observer who isn't affiliated with the NWS. Doesn't that make sense?!
CLE NWS is no more than a couple hundred yards from the runway at CLE. Certainly not an ideal spot for measure snow. But even in light wind situations they still are not accurate. It would seem to me that regardless of winds, CLE has an issue with snowfall reporting.