I know a lot of people subscribe to this theory but it just seems wrong to me. The liquid in the freezer will eventually stabilize to the same temperature as the ambient temperature in the freezer (given that it is not fermenting). As such I think you need the air temperature to be measured and controlled. Fair enough if you are worried about the constant cycling of the power on and off, with my Tempmate this is dealt with by setting an on value and an off value, and I believe it even has a minimum time between as an extra backup (which I dont think would even be required if the difference between the temps is >2 deg), perhaps the STC does not have this feature. However I think even a stubby of water is too much insulation for the probe. If you put the stubby of water if the freezer I would think that by the time it gets down to 2deg, the freezer will be at minus 10, by the time the stubby returns to 4 degrees the freezer will be at 15. I think you want the ambient temp swinging 2-3 deg, and the liquid temp will struggle to swing by a single degree.
Obviously plenty people are operating well on this model, so it must work on some level, but I have a probe just hanging 4 inches from the lid of my freezer, with no fan circulation at all, and the temp set on 2, and its been going strong for many years, temperatures perfect all year round. I think if you are fiddling around with a stubby of water and you have never tried just letting your probe swing in the breeze (or tape it to a bit of foam on the side of the freezer) its definitely worth giving it a shot, especially if you are having issues controlling your temps.