'Caveman' is pretty anachronistic for what they are talking about, the kind of diet they are discussing is a lot more recent than the Late Stone Age (Neolithic and Chalcolithic), grinding up acorns for flour is a lot later than people living in caves as their primary housing, they were in villages of hide tents and lodges using pretty sophisticated non-metallic tools by that point, not significantly different in technology from pre-Columbian Native Americans.
Real 'Cavemen' would be the Paleolithic - eating bugs, breaking open marrow bones and eating any scraps the predators left, any plants that didn't seem to kill the herbivores they hungrily watched, the occasional slow-moving or unlucky animal, and waiting for the seasonal floods to recede so as to get first crack at any stranded fish.