You are quite correct. My father built a log cabin (as a hobby I guess) and the fireplace had hinged arms that one could swing out over the fire or towards the floor. One attached pots on them (by their handles) and was able to cook or serve quite handily.
The hinged iron "cranes" you will find in colonial era houses are actually a deluxe feature--found in the houses of the rich.
Most typical (according to Janney) was a horizontal pole up inside the chimney supported at either end of the "smoke shelf" where a modern fireplace has the damper placed (a feature also absent colonial fireplaces). Such poles would only be found in the large kitchen fireplaces. Suspended from the poles were iron hooks, often banded iron with holes in them, allowing one to lower or raise the pot-hooks above the fire.
Kitchen fires, by the way, were not huge...even if the fireplace itself was 6 feet tall. That height and width was made so women (yes, they were the cooks) could easily get in and out to tend the pots. As evidence that they were not huge--I've seen several old kitchen fireplaces with the top lintel made of wood....so one would never make a fire with 5 foot flames, or you'd rick burning down the house--or burning up your pot-holding pole.