Lets assume Alice holds 100 shares of Twitter and wants to sell those shares on Open Transactions. Bob decides to purchase those shares. They decide the terms of the transaction, price etc and sign a smart contract. The transaction gets completed. Bob pays Alice for the shares either in dollars or bitcoins etc and alice transfers the 100 twitter shares to Bob.
How does one preserve sanctity of this transaction because, Alice can repudiate this transaction at a later date. On a parallel Centralized Stock Exchange the ownership of these 100 shares will still be attributed to Alice and she will continue to get dividends etc as an owner.