The Queen refused to allow the moment of her crowning to be filmed because she has a barmy belief that she is annointed by God. This concept is also important to her reasons for not retiring.
As far as I know, this is not the case, in particulars or generalities.
What certainly was not allowed to be broadcast is the period during the coronation ceremony in which the Queen and her bishops retreat under a sort of ceremonial canopy within the Abbey for ritual anointment with oils -- this is when the bishops 'elect' the Monarch as Supreme Governor of the Church of England, and is the bit that is usually taken as signifying the Monarch's link to God. (It's an echo of the ancient 'elected Monarch' ceremony).
Is this a personal belief by Elizabeth II or is the monarch being annointed by god a constitutionally recognised concept?
The 'annointment' is the one referred to above and has been carried out on every Monarch since time immemorial -- it's not described in any law or regulation, although it ties in with the Monarch's duties as described by the Coronation Oath Act (1689) -- this is the one that will give Charles so much trouble in a few years.
As for the Queen's personal beliefs:
The Queen takes her position as Supreme Governor very seriously, but whether she believes that she personally was picked by God is another matter and, I think, unknown.
She doesn't necessarily believe in a lifelong reign for religious reasons, although that might play a personal part, but certainly more because it's what Monarchs
do -- no-one wants to be a bolter like Ed VIII. It's a tradition that can't be broken. Edward VIII was a constitutional disaster and the very antithesis of a Royal role model. Not even George III was allowed to step down while insane -- the establishment put forward the Prince Regent to rule, but he wasn't made King.