Years ago I moved a tank and after smelling the sand decided to replace it. Not wanting to throw away the old sand I rinsed at as recommended above, dried it, and put it in some buckets. A few months later I decided to use the "clean" sand in another new tank. As water was being added an amazing amount of crud fouled the water and/or floated to the surface. So I stirred up the sand and siphoned out the dirty water. When I added more water it was amazingly clean.
My thought is that by drying the sand all the organic waste dried out also and would float in the water column making it easy to remove. Ever since any sand I wanted to reuse has been completely dried.