That's nuts. You should get avios and tier points no problem as long as they're not reward bookings.

Twitter was able to put my BA number on my reservation quickly and without any argument.

There is a policy about not being allowed to change it after benefiting from any AA status perks. Wasn't relevant in my case but they didn't ask anything that gave me the impression they were checking for that either.

I would recommend doing it in advance rather than relying on airport staff. Airport staff can change it easily but sometimes it doesn't propagate everywhere. And it'll make lounge access simpler too.