It looks like both the US and Russia screwed themselves. The US by its support of Muslim 'militants' in Kosovo and in Afghanistan, and the Russians by their support of other Muslim terrorist groups, not realizing that it would transfer to Chechnya.
I see all foreign policy as a chess game. Move and counter move. Angle for position, try and control the board. I think that in our case at least, we failed to calculate the moves and consequences far enough in advance. We were looking five moves ahead instead of the obligatory ten moves in the future.