Low-carb high-fat advocates generally do not eat grains and grain products due to the high carb content. They get their necessary fiber from non-starchy high-fiber vegetables.

Does the Bible Say We Should Eat Grains?
http://wellnessmama.com/2359/bible-grains/

The Real Problem With Grains
http://wellnessmama.com/575/problem-with-grains/

The real reason wheat is toxic (it’s not gluten or hybridization)
http://www.thehealthyhomeeconomist.com/real-reason-for-toxic-wheat-its-not-gluten/

The trick to recognizing a good whole grain: Use carb-to-fiber ratio of 10-to-1
http://www.health.harvard.edu/blog/the-trick-to-recognizing-a-good-whole-grain-use-carb-to-fiber-ratio-of-10-to-1-201301145794

Thoughts on the Kempner Rice Diet
https://intensivedietarymanagement.com/thoughts-on-the-kempner-rice-diet/

Wheat: The Unhealthy Whole Grain
Book Excerpt: Wheat Belly
October 2011
By William Davis, MD
http://www.lifeextension.com/en/Magazine/2011/10/Wheat-The-Unhealthy-Whole-Grain/Page-01?checked=1