The photograph is just a pathetic attempt by Murdoch Muckrakers to obtain a little notoriety and hence income. It should be discounted. The display by Elizabeth is just that of a small child trying to please her uncle David.
The discussion about the sympathies and actions of Elizabeth Duchess of York (nee Bowes-Lyon) is probably accurate - but at the time unremarkable for members of her social class. Her husband, Bertie, had been bullied by his father for showing signs of weakness - he was left-handed, for god's sake. Possibly as a consequence of the bullying, Bertie had a severe speech impediment.
Bertie's youngest sibling, John, was epileptic and autistic and was hidden away until his death at the age of 13.
David was shallow and selfish, but he was the idol of the masses and, in the public eye, could do nothing wrong. On seeing poverty in South Wales he said "Something must be done". This brought him acclaim for his compassion but he did bugger all about it himself.
He took the regnal name Edward VIII but showed his true colours by preferring the company of an American divorcee who (it was rumoured) had learned some cunning tricks in a brothel in Shanghai. If other rumours were true, she would need to use them because David had a very small penis.
Came WW2 and Bertie proved himself far better suited to kingship than his brother. The strain of kingship also proved fatal - he relied on tobacco and alcohol for support and died just 56 years old.
I am not a supporter of the monarchy but I do concede that George VI and Elizabeth II have behaved creditable in that role and that the photos of a six year old doing a NAZI salute do not bring credit to the "newspaper" that published them.