I'm waiting on the article to be delivered from my library. I'll let you know what it actually says.
EDIT: There are a lot of confounding factors, adjustments, and assumptions made in the study to get what amounts to a small but significant 2.3 kg/m change in BMI without explanation from calories.
Quick note: the microbiome is not mentioned in the article a single time. At all.
What they do show in the article is that they used information on caloric intake from 1971 - 1988 without corresponding exercise data because it wasn't available. So all of that is adjusted for, but the methods for any of these adjustments are not given.
Another thing that they had to adjust for was the change in demographics over the course of 40 years. When the survey started the respondents were nearly 85 percent white. By the end they were down to 45 percent. That's a huge change which was also accounted for somehow.
Another confounding factor which was accounted for, but hardly ever talked about at all and seems very pertinent to me, was the fact that smoking went from 37 percent among adults to 17 percent. That's a huge change in the use of a stimulant which has known appetite suppressant and weight loss properties which they just kind of glossed over.
They define exercise pretty loosely. They use the MET values which have some weird inconsistencies within them in the first place. Walking is a 3.8, doing gymnastics is a 4.0, playing Softball is a 5.0. That's a weird system. But basically exercise is then defined in how many times you do it per week with adjustments made for how strenuous it is. This is a huge issue because this exercise data is based on a flawed model, which is then manipulated further to compare exercise frequency with yard work and running by occurrences per week.
Finally, and hugely, the standard deviations on the BMI are all over the place and had to be corrected multiple times with regressions that amount to applied guessing. The information was based upon self-reported data in the first place and filtered out 90% of respondents to get the sample set.
So basically it's the same problem I have with pretty much every study that challenges the idea that people aren't perpetual motion machines. You don't get free energy to store as fat, or muscle. If you did, then you wouldn't have to eat, which means that you create energy within yourself somehow. People don't defy physics.
This article has a lot of confounding factors which are accounted for by making assumptions based on other articles which, with data that is incomplete, but they may be on to something if all their assumptions are correct. The problem is that you don't know what their assumptions look like because they are not a part of the published article. This is a huge problem for repeatability, so even further research with the same numbers might yield a very different result.