I think it is cruel to cause an animal to suffer, but if one comes up seriously injured, I think the humane thing is to put it out of its misery.
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Perfect. In this case, then, the folks, according to your calculus, did the right thing.
The dog is doing quite well after surgery, not suffering and no longer seriously injured.
They did “a” right thing, at least on the surface. Their response does seem financially irresponsible, however.