I do not believe that Gathering in any way improves the percentage chance that the fish you catch is going to be a specific kind of fish. I'm pretty sure that that is fixed: with a given bait at a given fishing hole, there's a 50% chance you'll get Fish X, 29% for Fish Y, 20% for Fish Z, and 1% chance for Big Fish Q.
I also don't think that Gathering improves the chance that a fish will slip the line - as long as you have enough Gathering to catch it at all. Each Big Fish has a certain amount of Gathering required to catch it. If you're under that number, ALL of that fish that you hook will get away, and you'll get a message saying that your Gathering is insufficient to catch that fish. Once you're past that threshold, though, these fish have a certain percentage chance that they'll get away when you catch them. For some, that chance is very high (like a 95% chance that upon hooking, the fish will get away), and for others it is much lower. I don't think that extra gathering improves that chance, though - ARR big fish with a high escape rate while fishing for them at level 50 STILL have a high escape rate when you fish for them at level 60. 10 levels worth of gear improvements hasn't helped one bit.
By the same token, I don't think having high Perception HURTS your chances. There are a lot of Fishers who believe that having high Perception results in Big Fish that are TOO big, and have a higher chance of getting away because of it. I don't think this is true at all. A record-breaking HQ Big Fish has exactly the same escape rate as a puny NQ Big Fish of the same type.
The only use for Gathering is to meet the "Can you catch this fish at all?" thresholds. Beyond that, it's all pure RNG.
Note that while I've said all of this, I don't have any concrete evidence to back it up. Fishing in this game is shrouded in mystery - unlike other gathering jobs, we're never told the chances of success or failure, and it's very difficult to see the exact effect that boosting various stats has on catching the stuff we're after. Any advice you hear on the topic should be taken with a grain of salt - INCLUDING the advice I've just given you.