Not sure if "meat only" can be a cure-all but anecdotally, I feel better when I reduce my gluten intake. I've never been diagnosed with a wheat sensitivity but my son has been forced to go gluten free because of one. When he is home on school breaks, we eat gluten free and I do notice a difference in how I feel.
I'm not giving up beer or the once a month pizza anytime soon but I have made conscious decisions to reduce my overall gluten intake.