You should check the load side of the fuse with a meter to assure it is powered (12 volts). I know you replaced the existing fuse with another one, but if there is a problem in the circuit, the new fuse could blow the moment you put it in thereby keeping the light on. Also, the only way to be completely sure a fuse is good, is to use a continuity tester (meter) the check it.
As far as the lights on the fridge control are concerned, you should verify the fuse in question is correctly labeled and indeed does connect to the fridge.
(stranger things have happened).
The only other thing I can think of at the moment would be a problem with the sensing circuit is keeping the light on. Though I have not heard of any problems with these myself, someone else may have more experience in this area.