[Thinlómien]

I'm too lazy to find the exact quote, but isn't Sam in Mordor dreaming about waddling through the river? If hobbits fished like standing in a river and piercing the fish with harpoons?

And of course, we're forgetting one of the most famous parts of the chapter of Herbs and stewed rabbit! Sam boasts to Gollum about S. Gamgee's fish and chips. That, if something, proves that hobbits ate fish.