Cross-chain communication is necessarily opt-in, so each chain can specify what you need to do to CTT with it. Two chains that are cross-tradeable have to both explicitly allow the other (whether directly or by some set of verification rules).
Also I'm pretty sure CTT does not mean that an asset leaves one chain and enters another, it just means two transfers on the two chains happen simultaneously and atomically (I send you BTS on BTSX in exchange for you sending me BitAPPL on BTSStocks).