[lambdadmitry]

Well, it can be solved the way current banks deal with fraud and chargebacks: rely on a very small number of parties misbehaving and set off a small percentage of money in the system to offset fraud. Another (complementary) way is a reputation system for "nodes" (as is the case in hawala). Both imply some sort of centralization, but so do Lightning incentives (see the discussion around "payment hubs"), so not much difference there.