How did Anna Anderson know things only Anastasia would have known? I don’t believe Anderson was Anastasia (they don’t even look remotely the same lol), but every documentary mentions it, even Anastasia’s family members and friends ‘recognised’ her. It really confuses me.
I am going to reference The Resurrection of the Romanovs quite often to answer this!
This ended up being longer than I expected, so if you want the real answer, just go down to the TLDR :)
So, first of all, most of the people who actually knew Anastasia in her lifetime did not recognize Anna Anderson. As the book details:
"The problem is that none of the recognitions of Franziska as Anastasia were particularly compelling. ... discount those who had at best fleeting or distant encounters with the real grand duchess ... do this, and we're left with a fairly weighty and impressive list of rejections: Baroness Buxhoeveden; Princess Irene of Prussia (despite allegations that she later had second thoughts); Grand Duchess Olga Alexandrovna; Princess Nina Chavchavadze, sister of Princess Xenia Georgievna; Princess Vera Konstantinova; the Gilliards--both of them, as we now know; tutor Charles Sidney Gibbes; Maria von Hesse and her daughter Darya, Countess Hollenstein (who undoubtedly had known Anastasia better and seen her more often than someone such as Crown Princess Cecilie); and former courtiers Nicholas Sablin, Admiral Federov, Anatole Mordvinov, Baron George Taube, and Vassili Woitinsky."
So, before we get to why people who did believe believed, I do want to talk about some of these people, and how they contributed to belief in Anna Anderson. (For this I'll be relying most on Peter Kurth's Anastasia as an example of the perspective of a die-hard Anna Anderson believer.)
Olga Alexandrovna is probably one of the pivotal points for both sides. Anna Anderson supporters claim she recognized Anastasia; they take her initial friendliness, letters, and gifts, as evidence. But this was more likely simply the kindness to a stranger, rather than recognition of family: she gave no signs of that in her letters, recognized no relationship, and used (writing in Russian) the formal "you". She would later say, "I know I should never have done so, but I did it out of pity. You have no idea how wretched that woman looked."
As for Alexandra Tegleva (the other Gilliard), Peter Kurth argued that she recognized her (the shared deformed foot being a main feature), but that as the wife of Anna Anderson's most vocal critic (Pierre Gilliard), was forced to remain silent. King and Wilson rebut this: Tegleva had, in fact, signed a statement rejecting Anna Anderson.
My own thoughts of this whole Olga Alexandrovna-Gilliard debacle is that on their first visit to Anna Anderson, the emotional shock likely made them more inclined to believe it was Anastasia, and to suspend disbelief for the present. Anna Anderson's supporters then used their reported words to act as though that was their true opinion. Some of it may also just have been plain lies from the Anna Anderson camp (who, for example, reported Gilliard as saying, "How horrible! What has happened to Grand Duchess Anastasia? She is a wreck, a complete physical wreck! I want to do everything I can to assist the Grand Duchess!"--he, of course, denied it).
Now onto the people who did accept Anna Anderson (I'm going to start with the most famous cases that often get quoted, except for Gleb and Tatiana, because they are the most confusing cases that I won't touch for now):
Crown Princess Cecilie: even supposing she was in perfect mental condition (which has been disputed), her recognition just weighs zilch. She barely knew Anastasia, and based her decision based off of the fact that Anna Anderson looked like Nicholas II and Xenia Alexandrovna. Also, she's just ... not very closely related, despite being the daughter of a Romanov.
Prince Sigismund of Prussia: Anastasia's first cousin, son of Irene. Now, this is someone who actually did see Anastasia regularly, but not after the World War broke out. He used a list of things Anastasia would know to identify her. Anna Anderson studied the Romanovs (I guess, maybe she has some similarities to us Tumblr Romanov freaks) through books, and knew a few things--that was, in fact, all that was required for Sigismund's test, which did not ask for her to be correct on everything. (You can find the questions--and some more explaining!--here.) She also spent five days answering them.
Lili Dehn: this one may be more of a shocker since Lili was so close with the family. But Dehn met Anna Anderson in 1957--Anastasia would have been 56, beyond easy recognition facially and physically. Like Sigismund, Dehn relied on details that would have been known to Anderson through published information--and even then, Dehn didn't get it right. She claimed that Anderson's three middle fingers, the same length, were the same as Alexandra's. (They weren't, as x-rays of Alexandra's hands make it clear--King and Wilson write it thus, as plural; they are probably right; personally I've only seen one--I've posted it here--yep, different lengths.)
Andrei Vladimirovich: I don't really know much about his identification of Anna, despite his heavy involvement in her case. However, King and Wilson quote him as saying, "I can't trust my personal impressions. I wasn't close enough to the tsar's children to be able to identify Anastasia".
Xenia Georgievna: another one I don't know much about. She seems to have been genuine and firm in her belief. I do not think she knew OTMAA very well, and relief more on what she thought a grand duchess should know, how she would behave (as a quick check I just searched through Azar's book for Tatiana for either Nina or Xenia Georgievna and Tatiana never mentions either of them).
Felix Dassel: this is another case of "person tries to use little details only Anastasia would know", except, as we've learned by now, many of these details supposedly only Anastasia would know have actually been published. And Anna Anderson made mistakes here--most notably, her adamant insistence that Nicholas II had no tattoo. Nowadays, his dragon tattoo is quite famous. She was also adept with words; when she didn't know, she could say something like "I know we gave presents, but I do not recall any longer what they were. It is so long ago. I cannot picture it. Watches, yes, but I do not think sabers. I don't know. Sabers? Sabers?"
Gleb and Tatiana: this one is honestly just a mess. I'm still confused. I still don't know. People have intimated money motives, or that they just didn't know Anastasia well enough. (They did not know her well, but probably enough to know if it was her or not.) I have no idea. To me, Gleb reads as a discombobulated man who genuinely believed he was doing the right thing (look at his Church of Aphrodite), but I'm not sure. He may have been discombobulated and knowingly doing evil, or maybe just discombobulated.
I hope this helped and wasn't a complete confusing mess to read! Thank you so much for the question!
TLDR: people who didn't know Anastasia use faulty tests to decide that it's her, based on family resemblance or her memories.