Sorry, but there are plenty of hunter-gatherers who don't eat fruit, because it doesn't grow where they live. Particularly in arctic and subarctic climates. Examine a traditional Inuit diet for example, which contains almost nothing but animal products.
Green vegetables, for their part, are a combination of cellulose and a few vitamins, usually A, C and K. They have no nutritive value, i.e. calories. The vitamins they provide are readily obtained from other sources. They can't be digested except in the large intestine, so the few nutrients they contain have low bioavailability. Unbeknownst to most of the public, they are the food product most likely to be contaminated with salmonella. The "fiber" benefit of vegetables and whole grains is supported by the same sort of studies you say usually turn out to be false. And theories for why fiber is supposedly good depend on the gut fermenting large amounts of starch, which doesn't apply to a carnivorous diet.