This is a slightly long but very interesting video on the subject of non-celiac gluten intolerance. Turns out gluten is in every grain, not just wheat, barley and rye. He explains the link between gluten intolerance and all kinds of chronic illness including thyroid disease.
Really seems to chime with what we're seeing with my daughter's symptoms. She experienced some improvement going (wheat) gluten free but nothing dramatic. She has tried giving up all grains a couple of times and felt significantly better, but found it too difficult so went back to eating "gluten free" grains and has experienced a marked deterioration each time.
I'd be really interested in hearing others' experience of going entirely grain free and whether or not it's helped.