oooooh it's been a long time since I've been set homework
Listen, if what you're saying is that the airline has insurance that covers it for passenger claims irrespective of fault, then that's fine and, in principle, the passengers can claim against it. However, there is no logical reason why that should be a contentious issue, requiring them to sue.
I note that Bealzebub states that commencing an action is simply the way it's done, but that doesn't make a great deal of sense - if the cover is there for the benefit of third parties, irrespective of fault, then why not just notify the claim to the insurance company? (to clarify, I'm not saying Bealzebub is wrong, just that it's an odd way of going about it).
If it's an application for some kind of declaration that you are a third party who is entitled to claim (as one of the passengers affected) then that might possibly make sense (though it would be a rather bureaucratic way of going about things). This is, however, a long way from what was being reported and what is being talked about on this thread, which suggested that the contemplated action by the passengers was an action against the airline arising out of an alleged breach of its duty of care.