The idea is not depending on them being.

Multisig + nLockTime transactions could do the job. First, we guarantee that the service operator is not able of running away with the money. With nLockTime we guarantee that, even if the operator disappears, the money shall come back to its rightful owners in, say, one month. I guess similar things could be implemented in OT to give the same guarantees concerning the assets.
Obviously, there's a long road to get there. nLockTime is currently not fully supported by the network. AFAIK BitcoinJS doesn't do multisig, and I know no other javascript client that could be easily embedded in a browser. I don't know if OT currently supports multisignature either, nor if there is a javascript OT client. Being honest, multisig isn't really essential. But multisig may also protect the user against a malware in their own computer. I find this important.

There's still an important trust issue that remains unsolved: the asset issuers. Established companies might not dare openly selling their shares in a black market. Actually, I wonder if any non-anonymous company would. And as we know already, trusting an anonymous issuer is a serious issue. There might be ways to overcome this problem too, but it won't be simple.