We're omnivores, and by grasses I mean the grains that they produce in any form (wheat, barley. Etc) I imagine there were wild fields of wheat that we settled near and cultivated. Is this era tied with the beginning of agricultural settlements, or did that come much later, tied with the cultivation of seed crops like we practice today?
While you might find some answers here, I recommend your cross post to /r/AskAnthropology as well!
I recently watched this documentary that talks about this very subject in the first 5-10 minutes.