Yeah. No.

As much as science knows anything, it knows that having too much body fat is bad for your health. Even the article you just linked states weight loss as its goal.

BMI is a crappy measure of body fat, fair; bodybuilders and athletes often have very high BMIs while having very little fat, but it's not "arbitrary" either. Doesn't matter much, since we have tools to measure body fat percentage directly. No need to use BMI at all.

Also note that article says to eat less "processed" food, but doesn't explain what that actually means. Is bread processed? How about a salad? How much dressing do I have to add to lettuce before it counts as "processed"? No answers here.

There's something to be said for the caloric availability of any given food, but it's pretty silly to say that you shouldn't consider them at all. People who are trying to lose weight need some measure of how much they're eating so they can be sure they're eating less. Until we have a better one, calories aren't going anywhere.

As for exercise, it is definitely important, but it simply isn't realistic to out-train a bad diet. It's not at all reasonable to say that exercise is more important for weight loss, and anyone who's actually lost a ton of weight will tell you as much.