Does leaving fridge doors open several minutes at a time lead to partial freezing of food?
You have it correct on how things work.
There is 1 piece missing: the evaporator.
When you open the door, the thermostat detects the temp increase and starts the compressor. The condenser cools the hot compressed refrigerant.
The cool liquid is then metered into the evaporator.
As the liquid expands, heat is removed, and the cycle is repeated.
If you have food touching the wall where the evaporator is it will freeze.
It is not a thermostat problem. It is a problem with things touching the super cooled surface. If there is an air gap between the area that is freezing that air gap will help to cool the box so the compressor will turn off sooner because the air is cooled.
So it is not a thermostat problem as much as an air circulation problem.
My refrigerator has the same issue. It is a side by side. The fridge is on the right. The left side of the fridge is where my evaporator is and if anything is pushed tight to the left wall it will freeze because the surface is well below freezing and the temp in the refrigerator box is still warm. Move the stuff away it quits freezing and works properly.
Since I do hvac work I used a thermal imager and photographed the evaporator so my wife would know the zone to keep open and we have not had frozen things in the fridge with half a dozen grandchildren raiding it.