If I do an Irish jig in front of my tank every day at 11:17am while wearing a hula skirt and singing "Walk Like An Egyptian" into a hairbrush, and my betta blows a nest, I cannot even begin to prove or disprove that it had any correlation short of setting up a large number of exactly duplicate tanks and providing a control. Even then, even the best designed of experiments have variables outside of human control. Is likely
that my jig and the nest had any correlation? When pigs fly.
If I feed my fish a new food and see a positive possible outcome with no other discernable changes in environment? There is a good chance that there is a correlation. Again, I cannot even begin to prove or disprove my theory without a number of tanks set up in exactly the same way and with exactly the same parameters and with fish of the same age and genetic material. And, still, there are variables. This is why scientists use very large testing groups and studies are run multiple times by multiple labs, to try to decrease the chances of interference by uncontrollable variables.
What I've found is precisely no different than what you've found. I fed a particular diet and have healthy, happy fish. You fed a particular diet and have healthy, happy fish. Neither one of us can prove anything. Ultimately I think that, in the world of home fish keeping, it is all AT BEST a game of making educated guesses at what will most benefit our fish and continuing the techniques that give us positive results. What I love about us is our never ending curiosity and desire to do the best for our fish that we possibly can!
And, honestly, you should see my Egyptian hula jig. I'm getting quite good!