Nice work, cool project and I could see this being really useful planning trips with friends / SOs. The first thing that comes to mind for me as a consumer is wanting more filters for Airbnb room types, hotels, flight stops, etc.
Calorie balance certainly matters but it is not that simple. Most leading health research institutions believe dietary quality plays a major part in health and weight management. Certain foods are associated with patterns of overeating.
https://www.hsph.harvard.edu/nutritionsource/best-diet-quali...
The average American diet has changed dramatically in the last century with the growth of the restaurant and food processing industry. Exercise participation has actually increased substantially in the last 20 years (https://www.cdc.gov/nchs/data/hus/2015/057.pdf) in the same time period obesity has soared.
Energy balance being responsible for weight gain is too readily used by the food processing industry in an effort to shift away blame for this epidemic.
You make a fair point on the quality of the research technique. I did skim through the study and conclusions and don't deny double blind randomized control trials are historically the golden standard of scientific evidence (http://ebm.bmj.com/content/early/2016/06/23/ebmed-2016-11040...). Other randomized control trials have found polyunsaturated fat in place of saturated fat reduces Coronary Heart Disease events (see this meta-analysis of 8 randomized control trials, n=13,000+ http://journals.plos.org/plosmedicine/article?id=10.1371/jou...).
It's no doubt an interesting study and makes me question recommendations to consume oils. Still, based on current scientific evidence, there is good reason to be cautious about consuming more butter / saturated fats as is being advocated in numerous comments on this thread. As a reminder to those reading, there is strong evidence to supports nuts are a much better source of fat for health than both oils and saturated fat. Here's a meta-analysis of two cohort studies of 110,000+ that found nut consumption is inversely associated with total and cause-specific mortality (http://www.nejm.org/doi/full/10.1056/NEJMoa1307352).
Like almost all nutritional studies, the evidence here is circumstantial and should be read with significant skepticism. Stephen Pauker, a professor of medicine at Tufts University and a pioneer in the field of clinical decision making, says, “Epidemiologic studies, like diagnostic tests, are probabilistic statements.” They don’t tell us what the truth is, he says, but they allow both physicians and patients to “estimate the truth” so they can make informed decisions.' (Excerpt from Do We Really Know What Makes Us Healthy by Gary Taubes http://www.nytimes.com/2007/09/16/magazine/16epidemiology-t....)
If you look at the larger body of evidence beyond this study, there are major reasons why institutional wisdom continues to advocate for the consumption of mono and polyunsaturated fats over saturated fat. For example, a larger 2016 cohort study of 115,000+ participants concluded high dietary intakes of saturated fat are associated with an increased risk of coronary heart disease (http://www.bmj.com/content/355/bmj.i5796).
Eating healthier is all about what categories of food replace current calories. If similar studies continue to show vegetable oil consumption is not protective against heart disease, it will probably make more sense to advocate replacing vegetable oil calories with fatty nuts and avocados that are much more nutritiously dense than oils (my preference for where to get fats). To jump to the conclusion we should all eat more butter based on this one study of n=9,423, however, is bad logic.