I've done this before so it's true. However I can't speak for later expansion packs as that was around the time Late Night was released. Recently I caught one of the new starfish without a bait, too. I think using the bait just increases the possibility of catching the corresponding fish, and of course its quantity. Say, when fishing in the Sunset Valley ocean, you can catch multiple types of fish - blowfish, jellyfish, starfish, shark, etc. - at random order. But when using a specific bait to catch, say, anchovy, you will mainly catch that fish and the chance of catching other aforementioned fish will be lower.
