Earlier quoted context omitted.
If it just told us that "fewer food choices lead to spontaneous calorie restriction", then both groups should have roughly equal results. They didn't. Any putative explanation of the results really needs to, well, explain the results. Not explain results other than the ones obtained.
Well, they did have roughly equal results if you look at the study. Both groups went from obese to slightly less obese. That said I don't follow your reasoning about equivalence. One diet was low carb. The other allowed for quite a bit of both fat and carbohydrate. Can't you see the difference?
In fact I'd suggest you consider this a clue... you're clearly explaining away, rather than explaining. "Explaining away" is in a way the most fundamentally unscientific operation there is... the fact that you're joined by a number of people who call themselves "scientists" even so doesn't change that.
(No joke. The fundamental breakthrough of science philosophy is that instead of asking the cognitively-natural "How can I prove I am correct?", science teaches us to ask "How can I prove I am wrong?" Everything else is just elaborations on that theme. "Explaining away" is one of the easiest ways to do the first, and is thus one of the easiest unscientific things to do. The fact that we've managed to train a great number of people who fancy themselves scientists but think their job is more about the first than the second is an indictment of our society, not an excuse to follow those people.)