Straws, I reckon- going by the US/Canada exception on the page that you linked.

That said, I have no clue how CX check-in would deal with this- there being no CX fares that don't have a baggage allowance..this will probably be as unique a case for them, as for this forum...hazy as it may sound, I'd just try to dumb it out (& if failing, nicely asking for the supervisor) unless you have wayy to much luggage to check in.