OC was an operator, they just didn't have a large enough aircraft for this contract so they farmed the work out to Island.
Not sure exactly how that plays out under US law.
It doesn't seem like an agent role. The transcripts are quite specific about the arrangements between the various parties.
It makes complete sense why they would be named in a case, as they clearly weren't operating as a proxy, they had an active role in choosing who the pilots were and so had a duty of care to ensure the service they were selling was safe.