But how does that work? The problem everyone has been bumping their heads against with the p2p concept is that nobody has a good way to know what's going on at the fiat end of any given transaction.
What's so hard about a simple check on that, using services like Sofort in Germany, that can check the fiat-user's fiat account? That can be cross-verified by other nodes who can see that particular account. So you get consensus.
(How to keep those consensus witnesses honest?
By freezing some of their own money to insure the transaction, unblocked when that one is successful.
Why would they participate?
To earn fees.)
Do this : go read up any whitepaper on crypto, trust, security, and when you see "trusted third-party", replace with "distributed proof mechanism".