I found this to be the salient point:

So who is telling these “misrepresentations of reality?” The originators would be the Russian FSB and the Kremlin, trying to tie in the fight against the Chechens into the American war on terror and legitimizing their operations in Chechnya. Many in the Russian media picked this up and ran with it. They were very soon joined by American journalists who were repeating the Russian journalists, and most importantly, the US Department of Defense. The DoD likely did so out of sheer ignorance (an ignorance shared by many stateside). However, it is possible that the desire to show Russia the need for an American base in Central Asia to support the war in Afghanistan was a motivating factor. Also, the US would like to portray the resistance to them in Afghanistan as coming from crazed Jihadis from far off lands when really it’s coming from locals and Pakistanis. This joined the Americans and the Russians in some mutually beneficial storytelling.