Wow what sector did you skip on and did AA realise what you'd done? If so they mustn't have cared and just re-issued a new eticket. I'd say the original CX flight coupons on US Air 037 or AA 001 ticket stock were probably suspended after you noshowed and CX probably could not unsuspend them without calling the issuing carrier but were within their rights to tell you to purchase a new ticket as per the fare rules.
Glad in worked out okay for you though.
we were originally booked from HCMC Vietnam (Ho Chi Minh City) to Hong Kong to take a connecting flight,
but we were staying in Hoi An and wanted to miss the extra flight from Danang to HCMC - thereby flying directly from Danang to Hong Kong so, I was just as happy to lose the business flight from DAD to HCMC and buy a one way flight from DAD to Hong Kong instead.
How did they know? I have no idea- I felt most likely it showed up on the computer screen. It was pretty worrying. I'm not sure that American were worried, as I said, in a very short time, the Advantage customer service re-routed the ticket and we were on our way.