Tigerlover, of many studies, this is the first I know of that makes this claim. I wouldn't bank it yet.
On a side note, judging by the way the many fish I've caught, cleaned and fileted have reacted, I would say they do feel some pain, but definitely not the level we do. I would say they are more sensitive to pressure than they are to something like a cut or a stab. In addition I doubt they can correlate whatever feeling they do have to injury or harm.
Whatever it turns out to be, I'll still be fishing, cleaning, filleting and eating 'em. They are too tasty to let die from old age
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Hmmm, pass the lemon and give me a beer...