The interesting thing about that study is that the low-fat diet had 8% fat, which is crazy low and a ~75% reduction, whereas the low-carb diet had 29% carbs, which is only a 40% reduction and not extreme at all. The studies that support low-carb being a more efficient diet have far lower carbohydrates than this study.

I mean, sure, if you just put people into ketosis with ~0% carbs it would be a different story! But 29% is on the other end of the spectrum. It is high enough that IMO, it makes the study's argument sound, but not valid, if you get my drift.

Not really, unless the diets controlled protein intake between the groups (which is often overlooked in low carb studies), low carb really just means high protein. in which case the beneficial results of the low carb group could just be because of increased protein consumption.

Yep, that would be another way to get relatively useless results, since protein metabolism is not at all energy efficient compared to carbs or fats.

So if caloric intake is kept constant at say 1500 but protein makes up a large proportion, "usable" calories is actually much smaller.

I don't think the TEF has a very large effect honestly. I think the other things that come with a high protein diet such an increased lean mass probably have a larger effect. Still in most low carb studies the low carb group is really just the high protein group. It's pretty obvious that you can't draw any kind of reliable conclusion if you change more than one variable