I would be humble when doing so as technically you're in the wrong and asking for a favor. Acknowledge the requirement for passport number on the test in their system, however then present everything you have from the process you have undergone with the authorities and that you (apparently wrongly) assumed that would be correct advice. I'd expect BA to put it back on the authorities tbh, or tell you it was down to you to check, I'm assuming the information on BAs system is also publicly available or it's not much use to the average traveller.