> When you're cooking a piece of fish, you're not changing its structure using heat and pressure so that globular plant cell structures are transformed into stuff resembling fibrous animal cell structures.

You are if the fish ate any plants before they died (and you cooked with heat, I'm vegetarian so am unfamiliar with the other poster's a la Ceviche).

And even if the fish didn't eat any plants, you're still changing the protein structures — this is even part of the point of cooking, as amongst other things this does, changing the proteins inside the food is a process that kills any bacteria and other parasites.