Annie-
Pierre Gilliard and Sophie Buxhoeveden did know Anastasia very well. I would even give grant that they knew her as well as Lili Dehn. However, I don't think it is tenable to say that Olga knew Anastasia as well as any of them. I have never read anything to the effect that Olga was a regular visitor to the Alexander Palace. As I understand it [correct me if I am wrong] for a long while, while the children [OTMAA] were growing up Olga lived in Kiev. As I have interpreted it [through the books I have read] though a close BLOOD RELATIVE Olga was not part of the inner circle. The immediate "family" [daily persona in the palace] consisted of Nicholas, Alexandra, the children, Anna Vyrubova, and Lili Dehn.
Concerning Pierre Gilliard- He was a regular in the palace, but as a tutor he was an employee, a servant of sorts- a high-placed servant, but still a servant. He would not have been considered a personal friend, with the same relaxed familiarity as Lili had with the family.
I have serious questions concerning Baroness Buxhoeveden and her rejection of AA. According to the literature that I have read AA accused BB of treacherously betraying the family in Siberia. As far as I know there was never any desire [on AA's part] to be recognized by Sophie. From the moment the Anastasia controversy began she [AA] detested her [Sophie]. If Sophie truly did behave herself, in Siberia, in a despicable way, there was good reason for her to issue a verdict of "not Anastasia." It covered her butt, so to speak.
As far as Ernie is concerned. Of course Ernie did not know Anastasia as well as did Lili Dehn. Grand Duke Ernest lived way off in Darmstadt, hundreds of miles away. During the time the children were growing up he was busy governing a country. He could not have seen the children any more than once a year. Lili saw them every day.
Just because someone is a blood relative, even a close one, does not mean as a matter of course that they necessarily are close to the person in question.
Case in point- In my own personal life if my mother's best friend or my father's brother were asked to identify me, my mother's best friend would be a far more reliable witness. She has known me since I was born, whereas my father's brother has never, EVER had a daily participation in my life. The same would hold true for Anastasia.
Now, as far as Pierre Gilliard is concerned- Whether one is pro-AA or anti-AA, it cannot be denied that he [Gilliard] behaved himself, during the Anastasia trials, in a perfectly beastly and unscholarly manner. Whether AA was Anastasia or not, Gilliard was in the pay of the Grand Duke of Hesse, and later on attempting to save his own reputation. He really did not care whether she was Anastasia or not, but was perfectly willing to sacrifice her, either way, for his own selfish ends. His behaviour, the last time he testified [before his death] proves this. At that time it was revealed that he lied, supressed evidence, and destroyed pertinent documents. Whether AA was Anastasia or not Pierre Gilliard's testimony of rejection is invalidated by the fact that he was a despicably petty and self-serving man.
I reiterate- I am not saying that AA was Anastasia. I am saying that either way, Pierre Gilliard's behaviour neutralized his value as a witness.
Another comment that you made- the comment that you would not accept or deny someone based on one person's testimony. I believe that you are using a double standard. You use the denial of Grand Duchess Olga to say that AA was not Anastasia, when Olga was the only close blood relative who ever agreed to meet her. That is the testimony of one person. However, you reject the testimony of Lili Dehn, on the grounds that she is "just one person."
Ultimately it doesn't matter whether you, or anybody else thinks that Lili was mistaken. What ultimately matters is that Anna Anderson was accepted as an intimate friend from long ago by Lili, and that the two "found one another" again. The fact that Lili believed her to be Anastasia ultimately means more than your questioning of the reliability of Lili.