Can you elaborate why the washout is irrelevant and what is loose about the study besides it being free living? The dietary changes that were instructed weren't highly likely to cause increases in fat oxidation to such a degree, except fasting and potentially alcohol reduction.

As far as i know, the additional 100 calories on their own shouldn't induce a metabolic effect like increasing fat oxidation by up to 40% and reducing carb oxidation. Adding 100 calories into the control would be nearly impossible to skew the metrics they were investigating.

Since you're a researcher, is the washout really irrelevant as the other guy says? None of the changes the participants would've made during the washout would have increased fat oxidation and they weren't restricting a lot except colorful foods basically. Since they were required to provide food journals they could be accounted for, and even if they did eat some anthocyanins without reporting, why would the fat oxidation rates increase that after the powder was given? Wouldn't the increase have been lower or non existent if they still consumed large anounts of anthocyanins during the washout?

The funding section of the paper says it was funded by the university's dean of research. The product was donated by the association. As another commenter that actually performs research mentioned, this is apparently pretty common for research.

You can actually just eat lot's of fruits and veggies and they activate the same pathway exercise and caffeine do for increasing energy expenditure. You would likely lose more weight than if you were to abstain from them.