It's worse than that ...

You have to use a third party which fetches the data for you ... So at least 1 third party but likely 2 third parties.

The way it basically works is that someone has a proxy contract to which they can post information to send to other contracts. Your contract trusts this contract to receive information, and therefore implicitly trusts the source to accurately query the information from elsewhere and send it to you.

However, this can be commoditised (e.g oraclize.it), and you could use a quorum of many different proxy contracts.

The trouble is that ethereum operations and transactions (especially involving storage) are expensive, and that there are much cheaper ways of achieving distribution and/or trust for many use cases.

I looked into this before. I just don't get it. There is definitely a trusted 3rd party in play which to me breaks the consensus model of having something decentralised. Maybe you can have many trusted 3rd parties and they all agree I don't know. But then insurance is a lot trickier than just paying out automatically when your flight is delayed. How do you even know the person took the flight. Maybe that doesn't matter. But lots of other questions probably do e.g. If we have a major event which delays worldwide flights would that bankrupt the insurance scheme. What capital must the decentralised insurance hold to be liquid. Who can recapitalise it if there's a black swan event. I am not against these decentralised models I just know there are a multitude of very difficult questions which insurance companies have already answered. P2P, decentralised and smart contracts can't be the answer alone?

I'm sceptical of Ethereum, but seems a bit too much to expect a proof of concept to include every nuance of current insurance theory. The question seems to be: is it impossible to model those problems using smart contracts? If not, it'll be done eventually.

it isn't yet. the current implementation relies on the flightstats API and oraclize.it to call the API from the contract. I think we are still far from truly decentralized applications, and it needs experiments like this to slowly get there. as a next step redundant data sources and oracles might help.