I lost weight: I went from 340 pounds to 214 pounds in exactly a year, and then bottomed out at 184 eventually (I've been purposely trying to gain muscle lately, which has been causing my weight to meander in the 190s since then).
My caloric intake hasn't changed in a way that can explain such a weight loss. I went from eating 1500-2000 calories a day to 1500-2000 calories a day (as in, no useful change, nothing that can explain 126 pounds in a year, disproportionately more of it towards the start than the end).
Now, what I did change was drop all grains (grains, cereals, pastas, soy, rice), drop refined sugars (I still use coconut and true raw cane sugars (Muscovado, Barbados, or Turbinado) or straight up raw honey; all very sparingly, and corn syrup is banned in my house), dropped seed oils (no more "vegetable", soy, corn, or canola oils; replaced with coconut and olive oil, or leftover bacon fat when I have it), and legumes (I'm allergic to peanuts, and don't care for beans, so the only thing I lost there is peas; soy is a legume, but I include it in with grains due to how it is typically treated culinarily, and thus already banned in my house).
So, given my experience, people are fatter because of reasons that cannot be explained by calories, such as chemicals in the things I quit eating causing unusual weight gain and halting the natural process of us burning endogenous fat. And it isn't like I'm the only person who did this, it is estimated over a million people have tried Paleo or some variant thereof and have significantly lost weight if they were overweight as long as they stuck with the lifestyle.
Side note: I went from 340 to 214 with chronically under-exercising. I still chronically under-exercise to a point, even though I now lift weights and try to go on daily walks. I still don't get the high other people seem to get from exercising. So, you can't use "increased caloric burn" as why I lost so much weight, it just wasn't there.