Welcome and sorry no one answered your question sooner. I only found it today. Perhaps others who saw it figured you had a pretty good handle on the situation already.
Most likely electrical continuity has been lost between the 12V blade fuse or ground block in/at the "electrical panel" and where the white and green zip cord wires terminate at the refrigerator terminal block. Hopefully the assembler of the RV did not splice the wires between those two points. Checking for power between the white and green wire is fine. However, the green wire (if it is the 12V power wire) should be checked for power to a know good ground. And the ground (if white) wire should be checked for ground with a continuity tester or ohm meter (alternately with a known good 12V source in the RV). As either the ground, or the power wire could be broken between the fuse panel and refrigerator terminal block. If in fact the refrigerator connections at the fuse panel are both good (power and ground) and one or both are bad at the refrigerator terminal block, a new wire will need to be run or the break found and repaired. Alternately since the refrigerator uses so little current and it has its own fuse protection, 12V power might be picked up from a nearby location instead of going to the effort to repair a broken connection as finding a bad splice can be difficult.