When a beer line rests on the cooling panel in my fridge, the beer will freeze in the line.
I was away for about 3 months a couple of years ago. The beer fridge didn't get opened at all during that time. Even after I had finished the keg there was still a large block of ice in the bottom back corner of the keg, that was the initial problem with no beer pouring.
In neither case was the fridge really that cold, normally about 2 -3 C depending on season.
On really hot days, the fridge works overtime trying to keep the thermostat (at the top) at the set set temp. Because of the temperature profile between the top of the fridge and the bottom, the bottom can freeze.