https://www.facebook.com/Anna-Anderson-WAS-Anastasia-Romanov-1587878578145622/
Are these people nuts or are they on to something? For my whole life I've believed that the Romanovs were brutally murdered and now I'm not sure what to think...
tldr: these people think that the entire family, or at the very least Alexandra and the kids, were evacuated from Ekaterinberg, possibly to Perm, and that the bones are fakes that were planted in the 1940s. Thus they think that all DNA evidence was fabricated as part of some conspiracy. I don't know how legit it is, but the "Russian Imperial Family Historical Society" also believes that the Romanovs survived.
There's definitely more to be said, but an old comment by /u/TenMinuteHistory links to the scientific paper showing DNA evidence that the bodies were the Romanovs, which you can read in full yourself, and which was published in a legitimate scientific journal. Elsewhere /u/mikedash briefly explains the context of the killings and links to a report by the commander of the execution party on what had occurred. The historical consensus on the murder of the Romanovs generally follows such authenticated accounts and DNA evidence rather than conspiracy theories.