Isn't this old news? I remember a comparative genetic study from about
5-10 years ago arriving at the same conclusion.
At least one study that found this (and is about this old) sequenced a numt*
of an African elephant instead of its actual mtDNA and therefore reached
erroneous conclusions, according to a later paper:
Therefore I find it rather surprising that the newest study puts the mammoth
back next to the Asian elephant.
* Nuclear copy of the mitochondrial genome. Occasionally mitochondria go
kaputt, and in those cases it can happen that their genome integrates into
the nuclear genome where it behaves like any pseudogene -- it mutates
without selection. Apparently such an event happened somewhere around the
base of Elephantidae.