I think you just got a dodgy reply - I find emailing BA a waste of time as you just often get boiler plate replies sometimes not even related to the question asked. (emails responses are answered 'offshore' I think). if you called rather than emailed I suspect you would have received a different answer.

My understanding is that the 2 week grace period is automatic- you don't need to ask for it- just call up after the flight and they'll backdate it.