I have the English translation of Radzinsky's "The Last Tsar". The photo in question is captioned, "Nicholas, Alexandra, Grand Duke Michael Alexandrovich, and his future wife Countess Natalia Sheremietevskaya frolicking on the deck of the Standart".
Yes, Johnny, the fault in this misidentification is primarily Radzinsky's. However, now that it has been shown to you that clearly the man does not know what he is talking about, it will become your fault as far as I am concerned if you continue to quote him as though he does. Capice?
For the record, neither Nicholas nor Alexandra ever met Natalia. As has been pointed out, she was never received at court. In the photo in question, I am quite sure the chap on the left is Nicky and the one on the right, Misha. I am not sure of the identity of either of the women in the photo. However, it is possible that Alexandra F. is one - but not that Natalia is another.
When Natalia was a Sheremetevsky, she was a middle class Russian girl who never met any member of the iF. She was then Madame Mamontov and after that Madame Wulfurt. After that, she was known as "Countess Brassova". She was never to my knowledge known as "Countess Natalia Sheremetevskaya", except in the mind of Mr. Radzinsky.