That quote is not in the "Anastasia Royal Diary" book. I own it personally and I am quite sure that it is not in there. The book does suggest that Anastasia did not really trust Rasputin, though...
On pages 102 and 103 it says:
"She's [meaning Anya Vyrubova] convinced he's a saint. Mama believes it, too, because Alexei always gets better when Father Grigory prays over him...I did dare to ask Mashka what she thinks about Father Grigory. She looked at me with her big blue eyes and said, "But he is a saint!"...Dear Mashka is so good! I must be evil to my very bones because I do not like this man, no matter what anyone says."
This is just a fictional book and I think that Anastasia really did trust Rasputin because of the letters that she herself wrote to him. I think that Carolyn Meyer (the author of this book) is just trying to "show the other side of Rasputin" through Anastasia's voice, if you see what I mean. I think that the author doesn't want the reader to just get a one-sided view of Rasputin as the holy man, the starets. By Anastasia having doubts about Rasputin's "genuineness" the reader gets to see what other people thought about Rasputin. But this IS just a FICTIONAL book. Although the book is a good one on Anastasia and the the rest of the family, in my opinion, there ARE inaccuracies. For another example, in the book in May 1914, Crown Prince Ferdinand of Romania and Crown Princess Marie are called King Ferdinand and Queen Marie, when in reality I think that they didn't succeed the throne until later in the year than May (not 100% sure about that).
