Had almost the exact same thing happen. I’m JAL Diamond with CX Green, and I usually book with my CX number for the miles, then show my JAL status at check in for the oneworld Emerald perks. Always worked fine.
But on a CX flight last month, the agent said they couldn’t give me priority boarding or baggage unless they switched my booking to my JAL number. First time I’ve ever been told that.
Not sure if CX changed something or if it was just that agent, but it definitely caught me off guard.