It's something I don't really understand, doesn't Lightning scale by bypassing what makes bitcoin what it is: the proof of work and no trust system? It seems with Lightning you are back to having to check every transaction, and because it's painful, the trust mechanism is being centralised. It's seems to me we are almost back to square one then (though at least in theory you can control everything yourself and do not have to distribute the trust).

No. It entirely relies on the guarantee that you can spend the Bitcoin transactions. Secure in that knowledge, it doesn't have to for every small transaction.