Which grain is NOT a primary gluten grain yet has been frequently avoided on experts' advice?

This grain is NOT one of the grains primarily avoided by those with Celiac Disease yet it has been frequently avoided due to the advice of experts. Do you know what it is?

Oats are not in the primary group of grains avoided by those with Celiac Disease but have often been avoided due to fears of possible Gluten-cross-contamination.

Source: Lapid, N. (Feb. 16, 2008). “Oats and the Gluten-Free Diet: Are Oats Safe for Patients with Celiac Disease? About.com. Retrieved April 16, 2009 from http://celiacdisease.about.com/od/theglutenfreediet/a/OatsForCeliacs.htm.