Can Freshly Caught Fish Remain "Fresh" for 2 to 3 Days in Refrigerator?

In my opinion 2-3 days is really just a guide to remind people that fish is highly perishable, more so than most animal proteins. Do not toss it in the refrigerator and expect to wait a week to get around to cooking it and expect it to still be edible.

From time out of water to cooking, it will greatly depend on variety, size, etc., but if it is properly cared for you will normally have longer than 2-3 days from catch. But, the longer it is from catch to cleaning, time is reduced, that is offal will deteriorate faster than flesh but damage the flesh if not promptly removed. Poor cleaning deteriorates the flesh. Any time out of optimal temperature storage, reduces useful time. You have no idea really how long any of these periods are, unless you harvested the fish yourself, so you assume reasonable handling and that from the time the merchant makes it available, you probably have 2-3 days before you risk spoilage and try to be familiar enough with your merchant that they have not already had it sitting for 2-3 days.

All of this though is non-optimal. Fish, and all seafood deteriorates fast. It is not like beef that often benefits from aging. Seafood quality goes down by the hour after harvest. If any seafood that begins to smell like anything other that fresh is past its prime at best. Sliminess, dullness of the surface, any loss of firmness, weeping of fluids, these are almost always signs that the fish is either past its prime or simply beyond usefulness. Some fish are soft to begin with such as salmon, but comparing two fish of the same variety, the firmer fish will almost always be get fresher or better handled fish.

Freshness isn't defined by time, it's defined by how good the fish is.

There are ways to tell without actually cooking and eating it, of course. If it's really fresh, there should be no fishy smell, and there shouldn't be visible signs of it going off. For whole fish, see How can I tell if fish is fresh? - fresh whole fish has bright skin/scales, and is firm. For fillets, again it should be more firm, it should be plump and not look dried out, and it shouldn't be starting to pull apart. In both cases, discoloration is a bad sign.

So the 2-3 days is just a very rough guideline. Honestly, it's noticeably less fresh after even 1 day in the fridge, and you should generally just buy and cook the same day, but 2-3 days is usually acceptable. This is all assuming it's fresh when you buy it. (As you mention, that doesn't necessarily mean it was caught just a few hours before you bought it, just that it was properly handled between catch and sale.) If it spent longer in transit, and wasn't well-preserved, it may not be good as long.

We have found that fresh caught fish. Gilled gutted thrown on ice in the boat. If placed in a lightly salted water in a closed plastic container will last 3 days in the 7 day meat keeper set at 32f. Or just at freeze. Often better than fresh froze as ice crystals damage tissue in meat. Or if wrapped tight water buffalo will be more tender after 7 days to eat.