Most cats aren't enthusiastic swimmers, except the Turkish Van breed, who are known to enjoy it. Even if they don't like getting their paws wet, cats will take advantage of any nearby streams or ponds for hunting purposes. I know mine does, though the amount of fish she gets is probably minimal compared with everything else (reptiles & amphibians, insects, birds, small mammals). With commercial cat food, she prefers the fishy kinds over the chicken and rabbit-based foods. She won't even go near the ones with vegetables in them.
A wild cat's diet would include not just muscle tissue, but also the stomach contents of its prey. It couldn't get by on plant proteins alone (being an obligate carnivore as Callaway has mentioned), but a small amount of plant matter is optimal for a cat's digestion. My furry girl regularly has a nibble at the back lawn, and she likes little bits of fresh wholemeal bread rolls.