Yep. I'm not saying one could support oneself through nothing but fishing (depending on a lot of details, of course). But I see no reason not to make that one component of a strategy for procuring food. And even if it only serves for a limited period of time (until your local fishing hole is all fished out), that may be enough time to bridge to the point where other options become available.

I think that ideally, one would use a combination of fishing, trapping, hunting, foraging for wild edibles, gardening, plus buying whatever food remains available for sale, to handle a shortage situation. Perhaps no one of those mechanisms is sufficient by itself, but the combination may be.