New Mexican Aztecs

Leaving Durango and driving south into New Mexico was an easy and pleasant drive through Cuba, close to Los Alamos and ending in Santa Fe. Close to the town of Aztec we saw a National Park Service sign for something called Aztec Ruins so we stopped in at the Aztec Visitors Center which like a lot of small towns in the USA has visitor facilities, including the all important restrooms, funded by the local chamber of commerce in a modern building just off the main highway. Two local volunteer ladies directed us towards the NPS site and off we went to find it. And what a fascinating few hours we spent there.
Briefly the early Spanish explorers into this area in the 1500s came across the site and incorrectly thought that the people who had built the structures there were Aztecs. Even though it became clear in years to come that the builders were actually the ancestors of many Southwestern tribes, the 'Aztec' name persisted. After a 30 minute film show in the park's visitors' centre which explained the known background of the builders of the site we went out and followed a carefully marked out trail that ran above, around and through the ruins. Originally built in the 1100s by the ancestors of the present day Pueblo people, the site may have become an important centre of commerce and religion in the area as the influence of the community of the fairly distant Chaco Canyon waned after 1100. Possibly because of a series of recurring droughts in the late 1200s the ancestral Pueblo people abandoned the site around the early 1300s and apart from treasure hunters in the 1880s, the ruins which were by now well covered with sand and scrub were not excavated until the early 1990s. What was found when the debris was removed was a remarkable series of stone built structures, some with wood and rush ceilings and floors still intact, one, two or three stories high, together with a variety of food remains, cotton and feather clothing, stone and wooden tools as well as jewellery made from obsidian, shells and turquoise. Associated with each group of stone 'houses' was a larger or smaller structure called a 'kiva' which is similar to the ceremonial rooms used by present day Pueblo peoples. And how the largest kiva in Aztec Ruins has been reconstructed is what concerns me.
Over a number of years the foremost excavator of the site, Earl Morris, decided that he knew how an original kiva looked and using this 'knowledge' he oversaw a reconstruction of the largest kiva into a form that he thought was how it had looked in the heyday of the settlement in the mid to late 1200s. While the reconstruction certainly is impressive the problem is that later scholars now dispute whether Morris's reconstruction is truly representative of what the kiva really looked like.
The question is should an existing archaeological site be rebuilt to represent what one person or groups of people think it looked like when it was first built or is it more responsible to leave a structure as it was found after excavation, not adding on any 'modern' timbers and stones. To my mind the reconstruction is wrong; a modern 'replica' could have been put up - or in this case it would have been more accurate to say could have been dug down as well as put up - but the remains of the original build should have been left untouched. But then, what do I know?