The microbiome of the gut is like the new frontier of medicine. It's currently very en vogue and lot's of interesting research coming out. For example, the link between bacteria population in your gut and obesity.
Diet can drastically alter these populations, and therefore when parents adjust diets (remove gluten, remove dairy etc etc) they are actually adjusting the gut flora.
The microbiome may be new, but treating children with behavioral issues with dietary intervention goes back 100 years (with varying levels of success).
The GFCF diet (and others) seems to get criticized because parental reporting doesn't seem to match scientific studies. But the anecdotal evidence is overwhelming. The Autism Research Institute has surveyed thousands of parents about diet and results, and some of the diets have a high success rate with helping some symptoms.
Diet can drastically alter these populations, and therefore when parents adjust diets (remove gluten, remove dairy etc etc) they are actually adjusting the gut flora.