Both background & substrate can affect a fishes color, in as much as the tone of that color. If you raise sibling fish under identical conditions, but change the background color between the groups using light color in some tanks, and dark in others, with some fish the difference is like night & day.
I have seen this many many times, with numerous species of fish.
Generally speaking darker colors such as black tend to deepen the colors & overall tones of the fish, lighter colors tend to brighten the colors & overall tone. The example above with Asian aros is a prime example of how that works when grooming young Gold crossbacks. The farms want to emphasize the high shine in their gold fish, so they use the white tank treatment. But quite often the end users (hobbyists) prefer the darker gold tones, which means the seller has to use black backgrounds to get the fish to show a deeper more bronze look. Again, it all boils down to personal preference.
So in grooming young fish, it becomes more of a personal choice than anything else. Same with adult fish. The entire concept of not being able to keep nice looking, colorful, and healthy FH in black background tanks is absurd. Some people may prefer to keep certain types of FH in lighter, brighter tanks, but that is nothing more than a personal choice based on their personal likes or dislikes. No doubt a lot of people that state that one can't or shouldn't keep FH in a black tank have never even tried it, and are basing their comments more on what they have heard, or read on the internet, and not by actually comparing the same fish under different conditions.
From a personal perspective, if I had to keep FH in a tank with one of those glow in the dark flowerly looking backgrounds, I'd stop keeping FH. But that's just me.