No single answer is 100% correct.
Could some paleo-men have been gathering some wild grains, such as the wild rice gathered by Native Americans... sure. And did they eat tubers... sure! In the season that tubers were available of course (tubers are very seasonal in most climates). But before the capabilities of secure, cool, dry storage the percentage of the diet that these foods made up was probably pretty small in the grand scheme of things rather than the basis of it.