If I say "you owe me $1000", and my Brazilian client says "no I don't", the current system offers a very speedy and cost-free resolution to that. We just have to do nothing, and the dispute will be resolved by default in favor of the client.

I can imagine a blockchain-like thing that would be able to shift the default action, so that I get $1000 or maybe each of us gets $500. I can't imagine a blockchain-like thing that could, without an oracle both of us trust, actually reach into the real world and arbitrate the dispute. (If there is an oracle both of us trust, there's no need for a blockchain; the $1000 can just go directly into escrow with that oracle before I start working.)