It seems to me GESP has invested a lot of time, effort and money in surveying, mapping and overall diving the Goodenough spring system. That in itself would make a lot of divers feel that it's "their" system and even though it's a public site they should be able to control who dives it and who doesn't (think Eagles Nest) but it's a public site and as long as you are trained, certified, experenced and respect other teams/groups established equipment you can dive it.
It only takes a small number of accidents/incidents/fatalities to potentially have a site shut down (think Eagles Nest) but based on the emails I have read and other information it seems to me that Cushman and Irons were qualified, asked permission and worked with the GESP.