They're not extinct. They're endangered. Otherwise, you wouldn't be seeing them in the wild. (Yeah, I know about the entire fossil Pokemon actually live underground thing, but those are different. As in, the creators of the 'dex actually genuinely assume that people can't just go out and find one in the wild -- or, if you'd rather go with the game's explanation, that they're really extinct and can't be seen in modern times without being revived from fossils, as the entire species is gone.)
Anyway, yes, I can believe it. First off, the concept of eating Pokemon really isn't anything new. They resemble animals, so some fans have no problem of proposing giving their characters something like Kentucky Fried Blaziken or Miltank burgers. Second, it's not like it's the first time it's been mentioned in canon. Ash was, at one point, afraid that Professor Oak would eat his Krabby, Meowth once tried to eat a Magikarp, James attempted to eat Togepi (before it hatched), and Miltank milk has been shown to be harvested for various dairy products.
Besides, the duck is carrying a leek. It's asking for it.
