I had a worker do this exact same thing with the exact same loads (strange), and I too wanted to find out why both appliances on opposite sides of the MWBC was damage, as in most cases the lighter load appliances opposite of the heavier load appliances will most times always fail but the heavier load appliance is ok , but the microwave failed and the refrigerator also failed, like in the OP the micro wasn't in use, so measuring the resistance of the failed microwave I saw why it took out the refrigerator, the resistance of the micro was .09 ohms, which meant almost a dead short, which would have sent almost the full voltage to the refrigerator.
What I found was when the wrong neutral was lifted the refrigerator being the heavier load first sent over voltage to the microwave damaging the control power supply causing the full wave bridge rectifier to dead short out, this then flipped the over voltage back to the refrigerator which took out its power supply and electronic controls, both of these controls are always on so even when not in use they will be damaged, but I didn't expect the flip-flop, and the only fuse in the microwave was a 15 amp slow blow, so it was enough to damage the controls in the refrigerator which I suspect wasn't running at the time, I think if the compressor was on line at the time it might have caused the 15 amp fuse in the micro to open, and might have protected the refrigerator, but that is just a guess.
but this was an eye opener, and the first time I saw damage on both sides of a MWBC.
I have since seen an even worst case at our city hall where a city worker was remodeling a bathroom, and went to tie in a new light in a junction box that seem to be in the right location right above the light, but when he opened the neutrals on a 120/208 3-phase MWBC, he floated neutrals going to all the EMS 911 computers and radios system, luckily for the most part almost all of them had dual conversion UPS and it took out the battery charges, again these shorted out which shifted the high voltage to the next phase which again took out these UPS and then the last phase was hit, all the UPS systems was dual conversion so the radios and computers are always running on battery power, and the charges just act as a power supply and keep the battery's charged, so most of the equipment wasn't damaged,
but three systems was, that had single conversion UPS which did supply utility power to the equipment, and the total damage was over $19,000, that was the end of the city ever allowing a city worker to touch any electrical.
Yea I know I ramble too much,:roll:
I just love to share things I have run into hopfully to help others when they run into the same problems.