It would be up to BA to prove that it was cancelled over 14 days before departure, not the other way around. They will know when exactly it was cancelled.
Do your flights not show up on Manage my Booking, but with a 'Cancelled' message?
I've had this happen to me more times than I'd care to remember. Thankfully I've always caught it early enough, and only once was there no Avios seat left (but got it released). But yes, completely ridiculous this keeps happening and phone agents have never shown any concern (or apology) - GGL team to boot.