Sure, you can't show that it's true for everybody but having a result like: "only 0.1% chance that it occurred by random if 2/3 of the population reacts this way and way less if it's half of the population" is very nice result to have.
If something occurs for 16 randomly chosen people (or even 15/16 or 14/16) you are virtually certain it occurs for very significant part of the population which is often the goal of the study - to justify further research.
It's not random. They were "sixteen overweight/obese men and women 30-66 years old, with a BMI between 27–50 kg/m2".
On their books, I think that would be a ridiculous thing to reject people's findings for. Almost every academic has written a book at some time. Instead, we need to recognize the possibility of a bias inherent in every researcher and look to the study design, execution, and conclusions to see if they hold. Phinney and Volek are in a different class when it comes to their books and their ideas than is, say, Robert Lustig.
Also, how would you run a double-blind test of the foods people are eating? It's pretty hard to disguise steaks ;-)
Most nutritional studies are observational, so the numbers are not very reliable. In this case, "subjects were provided with all food for 18 wk, which was prepared and packaged by staff in our research kitchen." That's one reason why the numbers were so small, though it would have been better if they'd been bigger.
The most reliable evidence would come from controlling what people ate and what they did. I'd have thought this would be something that could be done with volunteer prisoners.