I think Anastasia was buried with Alexei. The Americans' justification of Anastasia being missing from the 1991 grave as opposed to Maria was a lot more convincing, given that they made their assumptions were based on more factors as opposed to the Russians' computer programme. Bearing in mind the Russians who believe Maria was missing also said that the skeleton of Demidova was that of the Emperor - a very elementary mistake when it comes to forensics, I feel more inclined to go with the American assertion.
I also feel that identifying Anastasia in 1991, like King and Wilson suggested, may have spawned from the Russians' desire to prove to the west Anastasia was dead.