Of course, there is also the matter that specialist castes that are essential for the developement of civilization is essentially dependent on a stable food surplus, which hunter-gather societies will rarely be able to produce.
There's fishing, there's pastoralism, and one of the often overlooked and seriously underestimated possibilities, there's non-agricultural land management (encouraging the groweth of foragable food plants, discouraging nonproductive plants, hunting to extinction competing species). I'm far from an expert and I have serious doubts about the more edenic scenarios painted by American archeologists, but in Nothern European medieval society, forest management was such that even with an agricultural community in place, berries, hazelnuts and most fruit were not actually cultivated until the 13th or 14th century. Before that, they were gathered, and they played a major role as sources of fats, sugars and vitamins, so we're not talking about a marginal resource. Agriculture is vastly superior as technology, but it's not the only option out there.