I know very little about cross chain but it's interesting to think about. Forgive me if it's obvious, ridiculous or nonsense.
The idea works like escrow. Say A wants to trade with B for btsx with btc. A sends btsx to an escrow(C). C receives btsx and watch whether B has sent btc to A in specified time. If not, C sends btsx back to A. If yes, C sends btsx to B.
Here we can have the delegates(thus the btsx network) acting as escrow. That means btsx network need to know btc network. This is quite a burden and that's why it's not perfect. But at least btc network doesn't need to know anything about this. Maybe delegates can choose to directly use data from say blockchain.info.
The idea works like this:
A and B agrees on a crosschain transaction.
A sends a crosschain transaction (transferring 100 BTSX to B when a specified BTC transaction happens in 5 days).
B sees this transaction in btsx blockchain and is assured he can receive the btsx when btc transaction is done in time.
B sends btc to A as the transaction specified.
delegates see the btc transaction in 5 days, transfer the btsx to B.
if delegates don't see the btc transaction in 5 days, transfer the btsx back to A.