My $0.02 worth:
You're both right!
Individual quartz grains have low heat resistance... not a good insulator, but how the grains are arranged matters a lot.
Think about solid granite or concrete... very low heat resistance, made of quartz grains (and other stuff) all packed together. The key point is that there are no air spaces. Air makes insulation work. So if you make a layer of sand than maximizes the airspaces, and minimizes the contact between grains, then you have a good insulator (far better than the same mass of granite).
The best sand insulator, then, is made of grains that are all the same size (to maximize pore space), are round (so the contact between grains is a single point), and dry.
Adding anything between the grains changes the sand from a good insulator to a poor one - it replaces the insulating air spaces, and increases the number of contact points between grains that conduct heat. If you fill in all the pore spaces with smaller grains, you have rammed earth - poor insulator, but excellent thermal flywheel.
So you can find, or make, sand with a wide range of insulative properties, by choosing the moisture, particle shape and size distribution. Dry, well sorted, round-grained sand = good insulation... wet, unsorted, sharp sand = poor insulation.
For the purpose of making a floor with high heat capacity and low heat resistance (high conductivity), sand needs some help - sharp sand is a little better than round, a mixed range of sizes is better than well-sorted, and adding a little silt and clay helps a lot to fill in the interstitial air spaces to increase conductivity.