In the realm of international air services, CX is a "Hong Kong" airline, not a "Chinese" airline. Hong Kong negotiates and signs its own air services agreements (ASA) with foreign countries; so, if Cathay is not a "Hong Kong" airline, it will be cut off from whatever traffic rights is available from those ASA's.
Cathay has flown into mainland China before, with scheduled services to Shanghai. It was only dropped when they took a majority stake in Dragonair and KA took over the routes. It is no secret that CX now wants to re-establish service into the mainland, and the "direct" service that is being rumored might just be some same-flight-number-via-HKG deal, if and when China service does resume.