Yes, yours is the correct solution.I agree. It was a no win situation out of the gate, and imo not the fault of the shop. Devil's advocate here: I would have explained to the customer it had nothing to do with any work the shop performed and stood firm. Had it gone to court I'd hope the people hearing the case have half a brain. The mileage on the vehicle and other evidence the shop could dig up should help, then hope for a ruling in the shop's favor and move on. If I lost I'd pay as per the ruling. As in life everything passes, and this too shall pass, including the bad PR no matter how it was handled.
Replacing the engine is not going to stop the average Joe from saying they blew up my engine and put a used engine in it, I'll never use them again. Or the possibility of the customer saying they did the right thing, but people hearing the story thinking they'd rather not take a chance dealing with that shop.
Still having grown up in a small town I completely understand the shop owner wanting to do right, which is why buying the car might work. Probably cheaper than the lawyers retainer.
Either way what there doing now is the absolute worst solution IMHO.