Humans are classic examples of omnivores and, in fact, their digestive systems are very similar to those of carnivores. Herbivore alimentary canals contain a "bioreactor" in which bacteria digest plant components such as cellulose. (Mammals, even herbivores, cannot do this unaided.) These compartments include the appendix of the rabbit and the cow's rumen. Humans have no such structure.
Herbivore teeth grow continuously throughout life as an adaptation to the wear and tear of eating tough plant material. Carnivore teeth, adapted to a softer diet, have no need of continuous growth.
As for a fridge being an essential requirement for meat-eating, medieval man seemed to manage with salting, smoking and pickling.