With the extensive troubleshooting I just completed with a Pool pump tripping a GFCI breaker instantly it has to be something in the wiring on that specific receptacle/circuit causing the issue. The way a GFCI works is by monitoring the difference between the HOT and NEUTRAL terminals (keeping in mind the neutral is connected to ground) this is why older houses that have Knob and Tube wiring it is acceptable and code (in our area anyways) to have a GFCI breaker/receptacle supply this circuit as there are no ground wires within the circuit.

Are you positive that you have a GFCI receptacle and not an AFCI receptacle? With older appliances (and some newer cheaper appliances) they do not have efficient motors in them (mostly AC motors) causing an ARC at startup and tripping the circuit (an ARC between HOT and GROUND).

In any case a Fridge must be a dedicated circuit and does not require GFCI/AFCI protection. Depending on the area most places allow a duplex receptacle for the fridge as it is typically enclosed within a cabinet so using it as a general purpose plug is not easily achieved. If the circuit is located in an area that the plug could be used as a general purpose plug as well as the fridge then I can see an inspector requesting a single receptacle to eliminate the opportunity to plug something else into it.