Yeah, I gotta agree with other commenters that the methodology is pretty weak here.
Seems like the challenge would be to separate “paying more attention to your diet (any diet)” from “following a specific diet”. Like a variation of the Hawthorne effect; the mere fact of knowing you are under observation can make you feel better, in the short term (three weeks, per the article!).
Like, if they did the same study using the “South Indian Diet” or “Mesoamerican Diet”, would they get the same results?