The majority of paleo-omnivores "cheat." Most of them still use oil (lots of oil!) and many more still consume dairy products (sometimes raw dairy, but mostly pasteurized) and quinoa.

I also found several small groups of omni-paleos who were regularly eating legumes! So, perhaps true paleo isn't possible for anyone? Or perhaps this suggests you can be vegan-paleo and "cheat" with legumes and quinoa like everyone else if you want to...

The caveman diet, also referred as the Paleolithic diet, is a diet with an odd concept and aimed to mimic as closely as possible the way our caveman ancestors ate. More than ten thousand years ago, the period was called Paleolithic period during which the human ancestors were hunters and gatherers. They consumed the foods that they could find in the wild, including vegetables and fruits that grew locally. During that time, everything was consumed raw and milk & other dairy products were not obtainable as animals had not been domesticated.