Considering how fast fish without refrigeration would spoil back then, the rarity of access to sugar and the need for energy dense foods, "fish bad, sugar good" makes perfect sense.
People dried and salted alot of food to preserve it. But fish already live in a world of salt, and so I wonder of worms and parasites still survived this proxess. And I think a lot of salted food was just eaten, not cooked?
As always, dose determines toxicity. While alive and in salt water fish are pretty good about regulating their internal salinity and the parasites that live in them enjoyed the benefits of that regulated environment. When dead and packed in salt, fish are noticeably less able to maintain homeostasis and the concentration of salt is enough to pull the moisture out of both the fish and any parasites via osmosis. This kills the parasites, though there may be some cases where eggs survive that I'm not aware of.