There is a LOT on this in the threads here, it's all been gone through, fought over, etc.
Sigh. Let me see where to start to summarize. At this point I'm not even sure if her parents were alive at the time due to confliciting stories. She was reported missing in 1920. Recent findings claim her family thought she was killed by a serial killer because there was one in the area, but no evidence was found. Then her name came up years later during the AA trial after a private eye hired by GD Hesse (Alexandra's brother) broke the case that the "Anastasia" claimant from the asylum was the missing Polish factory worker. There was and still is much fighting over this, but the 1994 DNA results show it's very likely she was related to FS's great nephew (and not at all to the royals.)
I guess her family wasn't all that close to her and didn't look too hard.
The story goes that the siblings first recognized her then denied her after talking to her. Some say this means she wasn't their sister. Others, like me, believe they denied her to avoid financial responisibility for her and not to expose her and ruin her 'career' as "Anastasia." There are letters and comments by the family later that back this up. So that satisfies me. I could totally see my siblings denying me if they thought I was going to be financial burden to them. There is also a letter from her sister Gertrude's lawyer years later telling her she no longer had to worry about having lied when she said she wasn't her sister, the time had expired and she couldn't be prosecuted. Apparently she'd spent years worrying about it.
I have no doubt at all that AA was FS.