I think the only way to know for sure would be to convince him to do at minimum a month of faithful paleo - without sugar, flour, fruit, and even nuts and dairy (perhaps except for ghee and butter). Of course you mentioned that he is already resistant to food logging, so you'd may have problems convincing him to give up that last 25%. If he did a month like this and weight started to melt off, it could become apparent that even though quantitatively his nonpaleo intake was 25%, it was having much more than 25% effect against his weight loss hopes. (And as Ignacio mentioned, and I will attest personally, just 25% of neolithic elements is enough to throw off efforts entirely.)

Also, I didn't see any mention of intermittent fasting - maybe if he combined intermittent fasting with working out - and he did his training sessions fasted before getting his carbs (= friendly carbs like sweet potatoes) in, perhaps there could be some results? I've read enough testimonies from folks who had no luck losing weight until fasting was integrated strategically that this might be key for him.

Finally, one other succint list of causes to consider: Mark Sisson's 17 Reasons You're Not Losing Weight.