If I'm understanding what you were told correctly, it's plain not true. One could argue that what you have already caught influences what you can catch still in that bucket, but it doesn't happen like how you were told.
We'll take A bait for example: When you use an A bait, you have 9 large fish and 18 medium in lake. If you catch a large fish, there are now only 8 left. It does NOT mean that simply because you caught a large fish, the next thing you hook will be a medium or a small.
Say you catch 4 more large fish, bringing your total to 5 in this bucket. Now there are only 4 large left in the lake for this bucket. That would mean that you are less likely to hook more large fish than when you started your bucket. It doesn't influence what your next potential hook will be beyond that. The game basically does a "bite check" at set intervals. Depending on what distance you are out, it will pick a random number within the allotted range if you get a bite, and that number will determine what the fish or junk is that is hooked. It's more complicated than that, but the idea was just to let you know that it's random within the other conditions, not as you were told by this random user.