This is just not true in the bigger picture of human evolution. That paper focuses on humans in North Africa 15,000–13,000 years ago which is a very tiny snapshot in time and geography.
Eating meat is a major part of what separated archaic humans from other primates; it is theorized that the calories from meat is part of what helped us grow our larger brains. Homo Habilis was eating meat 2.6 million years ago, well before Homo Sapiens even existed. Homo Erectus hunted to the point of wiping out many large herbivores over a 1.5 million year time period. They are meat regularly enough for tapeworms to speciate specifically for us as hosts.