Thermal mass, my man.

Air will fluctuate temp much faster than water.

The fridge will be working to get the water chilled but if it was empty space than it'd be working to simply chill that air too, plus whenever you open the fridge door, all the cold air falls out the bottom - heat rising and all - so the compressor ends up working more on an empty fridge. Whereas if you chill 35 12oz bottles of water and open the fridge door, you'll lose the air (but there's less of it) but yr not gonna effect the water temp.

I built my fridges from chest freezers which I got for free off Craigslist. I used freezers since they're more effective getting to lower temp, and basically set them on their warmest setting. One compressor for the fridges, which are directly underneath my counters. The counters themselves are hinged and sealed, they lift up and are the door. I have 5sided sealed and lidded drawers along the bottom. You pull them out then lift the lid, like a box with one side the outward face of the cabinetry. Those are the freezers, with their own compressor. Insulating a box isn't rocket science, and transferring the compressor and radiators isn't difficult either, just know what your dealing with and the particular chemistry of your units. Don't kink lines, etc.

Reach in (down) fridges save a TON of electricity.