Not really...it depends on the fish, what it ate, and how it was raised. Farmed fish have the potential to be as bad as farmed beef. Whats scary is that most people eating junk farmed fatty fish think they are eating healthy but they are not. As a general rule, the fats in grain fed-factory farmed animals (including fish) are basically bad, so you want to stick with really lean meats from those sources. One the other hand, most wild caught fish, hunted animals, or animals raised with their natural diets (e.g. grass fed beef or sheep) have a very different omega 3/6 ratio, so fatty meats are good.

Also, based on your post, vegetarians must only eat rocks if they avoid things that live.