More on the "other components" issue -- a lot of people have issues with some of the fermentable carbohydrates (e.g. fructans) in wheat, which also happen to be present in the other gluten-containing grains. "Have gas" is a bit of an understatement. For some people this can lead to cramps, vomiting, and other fairly severe digestive problems.

So people on the low-FODMAPs diet end up using "gluten free" as a convenient shorthand for "doesn't contain these particular grains".