They couldn't have gone off the remains, because the body marked Anastasia is around 5'7" and the one they just found is around 5'3". I think they must have gone off some earlier measurement or from photographs.
The American forensic scientists used measurements from the skeletons' femurs and arm bones to estimate the girls' heights. And I stress 'estimate' because by the time Dr. Maples examined the remains, he was "horrified to see that some of the long bones of the thigh and arm had been cut in half; this could only make it more difficult for him to estimate height." [Massie, pg 60] To my knowledge, the American scientists only referred to photographs to help differentiate between the girls *after* they'd estimated the skeletons' height.
Although the media persists in labeling the newly found remains as belonging to Maria, there was significant disagreement between the forensic teams about the identification of skeleton #6 -- some of it centered around the height discrepancy Aliss points out. The Russians believed skeleton #6 belonged to Anastasia, and the American team believed it was Maria. Apparently Dr. Abramov based his findings primarily on facial reconstruction and superimposing photographs, while Dr. Maples considered height, development of the vertebrae and pelvic rim, and development wisdom teeth.
Reading pages 63-67 of Robert Massie's
Romanovs: The Final Chapter convinces me that the height of skeleton #6 is correct, but the identification as Anastasia is wrong.
I also have a Russian book which presents
a forensic examination of the remains. The vocabulary is difficult and specialized, but I'll see if I can find any additional information on the girls' height from that source.