People have no concept of economics. There's a steady level of demand. It's not possible for prices to rise and demand to fall. As the supply of fish declines, it is demand staying CONSTANT that causes the price to rise. Sure, fewer people are willing to pay the higher prices, but as long as there are more people willing to pay that price than the remaining supply of fish, it is in the economic best interest of the commercial fisherman to keep going out to wipe out the last remaining stocks of an overfished species, since he's getting so much $$$ per pound.
The original article is a bit confusing regarding tuna. When they talk about overfished they mean bluefin tuna....good luck finding that in your local seafood market, most of it is going to Japan for a zillion dollars a pound. Yellowfin (chunk light) and Albacore (white meat) tuna aren't particularly overfished and can be bought relatively cheaply everywhere.
There IS a point at which high prices will drive down ANY demand. And that IS basic economics.