And you are also incorrect that both groups had equal results. There was an 8 pound weight loss difference on average. Did you even read the article?
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.)
Curious if you could name one food that was particularly difficult to cut out.
I've tried many times to cut out chocolate, and managed for up to 6 months at a time before coming crashing down. A few months ago I switched to "mindful eating", which says I can eat chocolate whenever I want, and life has been better.
Sticking to these diets is the hardest thing. I spent a few months on a paleo diet and got a bunch healthier, but it was really hard to find things to eat, and pretty expensive as well. I don't think dietary changes are worth it unless you can reasonably stick to them for the rest of your life, and anything that says "no X ever again" is likely to fall into that category.