That is not the fish per se but the fish raised in our horribly polluted oceans. It has been shown that Mercury concentrations in fish respond quickly to and track levels of industrial pollutants.
So, I stand my my contention. Before the Industrial Age there were many populations where Catholics and non-Catholics existed side-by side and ate exactly the same diet except that Catholics had "meatless days" on which only fish could be eaten. I am aware of no retrospective study, and I have looked, that shows that Catholics did less well because of this. If you can find one, I would be grateful for it!
And as you say, in most fish oil products, Mercury has been depleted. (I would not trust any coming from China, though - its more likely to be waste motor oil than fish oil given their record.)