I tend to agree.  My two successful revivals of dead or non-cooling refrigerators were 1) Re-attaching a wire, and 2) Replacing a small broken spring.   Both machines had been cooling fine, so refrigerant loss was never considered -- YMMV with an unfamiliar fridge.  I think this sort of thing is more common than compressor failure on vintage refrigerators.  Travis has demonstrated this with his skill at bringing monitor tops back from having been left for dead.

The one dead fridge I sadly couldn't diagnose was the beloved little 1939 Westinghouse I got for free in the mid-70s.  It ran almost continuously until the spring of 2008.

Ray, the '39 Westy just went completely dead one day.  It had spent its final 20 years or so keeping drinks cold on the covered patio at my mom's house.   Mom had been placed in a skilled nursing facility and I'd regularly swing by the house to pick up mail, pay bills, etc.  I noticed that toward the end, the fridge would sometimes be running and cooling while at other times it had defrosted itself, so my gut feeling was that it was an electrical problem and not a gas leak.

At the estate sale, the fridge was sold to a guy who felt he could get it running again.  I hope he did, because if the compressor was still good, that faithful little box didn't deserve to go to the krusher.

Hell, they only plugged it in for five minutes. That ain't near enough time to decide if it's going to work. May be nothing wrong with it.