Spot on in general, I'd say, but I was always under the impression that the ancient greeks didn't have a large body of priests (Delphi being distinctly unusual) in this regard. Otherwise, their temples did not require the intervention of a priesthood between worshipper and worshipped.Take the Norse, for example. While they had a priest type figure, called a godhi (I don't know how to represent the Scandanavian characters I need), but he was much more of an adviser/organizer/loremaster figure. When the Norse held a blot, or a sumbel, everyone joined in with toasts and boasts and oaths. If the godhi were even necessary at these types of rituals (and often they weren't) it was as the guy who planned the event. The interaction between the Aesir and the Norse, however, needed no intermediary.
The Greeks, as another example, had huge temples staffed with priests, but the religious sacraments (animal sacrifices and the like) were usually either carried out directly or sponsored by individuals. Generally there was a huge feast after a sacrifice, where lots of people were invited, but the religious component was often between the Olympian and the particular Greek directly.