Well, everything (re medical) would be paid here for everyone without any questions - because everyone has got a medical insurance.
(Of course, the [different] insurance companies will try to get the spent money back from the company of the causer of the accident.)
The one other thing to consider here is that once a lawsuit is filed, most insurance companies put everything on hold waiting for the outcome of the suit. It is for that reason that most personal injury attorneys wait until medical treatment is completed before threatening and/or filing a lawsuit. That way they don't hold up medical treatment for their clients.
I don't know in the Staten Island Ferry case, but the attorneys may have been so eager to file suit (maybe before somebody could woo their clients away) they jumped the gun and made it impossible for the insurance companies to take care of the injured people.