GFCIs don't kill refrigerators. A certain percentage of refrigerators will develop leakage currents over time whether they are plugged into a GFCI protected circuit or not.
All of the refrigerators with this defect that are plugged into GFCI protected circuits will eventually start tripping the GFCI, but the ones that are not on protected circuits will show no sign of trouble -- possibly for many years -- until they either give you a nasty tingle or fail to a dead short and blow the breaker.
So to a refrigerator repairman, it seems like most of the refrigerators with "compressors shorting out" are plugged into GFCI circuits because those are the ones that give an early warning of leakage current and are amenable to repair before total failure. As JimmyJames points out in comments, I'm suggesting that the repairman's belief is an example of "survivorship bias".
In the best of all worlds, a refrigerator should be on its own GFCI outlet so that nuisance trips from other outlets will not cause the refrigerator to lose power.