I think it's based on studies that attempt to correlate certain symptoms to high or low gut bacteria.
Yes, but my point was that without qualitative data and proper controls, it's probably fairly easy to make a similar list in response to anything: astrological stuff, letters in a person's name, weather in the area, or maybe even the microbe strains in someone else's gut. If you present random data in just the right way, people will see patterns in it that fits their own expectations. I think if you replaced the symptoms list with a list from astrology ("You will be unlucky in love today." "Beware of solutions that look too easy."), you'd still get plenty of people who would be convinced that the predictions are accurate.
I've just started reading a book: Standard Deviations, Flawed Assumptions, Tortured Data, and other ways to Lie with Statistics. I wouldn't be surprised to find an example similar to the microbiome results vs people's seeing correlation just because they expect it. If you want to believe that the test is accurate, and it says you should expect 'bloated feeling', is it all that unlikely that your fallible memory will 'remember' feeling bloated the previous day or two, even though you didn't notice it at the time, or that you'll re-judge 'normally full' as 'bloated'?
If a properly-controlled study found that a 3:1 ratio between strain x and strain y has a 63% likelihood of the patient having a conversion of dietary iron to the usable form 34% lower than average, that would be useful. Vague predictions that can't be qualitatively verified aren't very useful.