My non-primal DH (5'10" and 160 lbs on a good day) has some gastro issues too, although it's not usually fatty foods that bother him. We think it might be undiagnosed IBS, but doctors have been useless and insist he's the healthiest person in the country despite his gastro issues, crappy immune system and a host of other things. He's pretty much voluntarily dropped grains (except a slice of toast in the morning and the occasional bowl of cereal) but this hasn't resolved his issues. Have you looked into the possibility of him having IBS or other ailment?
Also, what is oily meat? I gotta say, that doesn't sound appetizing to me, and my stomach could digest rocks. :-)