Phew, for a moment there I thought he was actually going to provide a satisfying answer to one of his plot holes.
The explanation is simple - ‘The Day of the Doctor’ doesn’t take place in 2013. Go and watch it again. We are never given an exact date for when the modern day portions of the episode are set. Without an exact date there is no plot hole.
I’ve also just remembered that we were never given an exact date for ‘The Power of Three’ either. We’re given months, but not years.
The only date we’ve got certain is that the Name of the Doctor is set in 2013 for Clara. We also know that when Clara met the Doctor she was probably 24 (going by the ages written in her book) and now she’s 27.
You’ll probably have as much luck figuring out the dates of everything set in modern times post Let’s Kill Hitler (sans Name) as you would sorting out when UNIT was established or whether or not the second half of series one is set in 2005 or not.