I do not think I could remember exactly how we celebrated each of our children's birthdays 20 after they happened. I might remember that we celebrated a birthday wth a pizza or a visit to a circus, but I would not remember which birthday. Was it the 7th birthday or the 8th. And that would be even more true for parties DC attended as guests.
However, if you are the kind of person who has a private secretary or private office, then all your official appointment diaries will be kept, not just chucked out at the end of the year like most of us. Personal engagements would probably be registered as well to stop double bookings.
All PA has to do is produce his appointment diary for the relevant year and show us the entry on the relevant day. It may not note exactly where he was, but it would register that was Princess B/E's birthday, taking her and friends out 3.00pm onwards.