(from an outsider) One aspect of humans is that: The more money they get, the more likely they are to forget where they came from and the nature of being an employee. Note I say 'likely' not all. They can quickly get used to having things at their disposal and believing that they know the correct solution - after all is that not how they became successful and wealthy?
It may well be that the option of local medical support whilst the patient was stabilised was not fully considered and the rush to 'home' in the USA began. If it turns out that no flight plan was filed, that would indicate heavy pressure to 'fix it on the run'.
No surprise that Bahamas handed this off. They do not want to be the ones to find fault with an American of influence.