Chris: your critical poster should be aware that ANY heading fluctuations such as are typical for a cross wind takeoff will allow the FMS to try to compute a wind direction - however it will be in error!
This feature was often seen during base training when the trainee had insufficient/too much rudder in for asymetric flying. You could watch the W/V readout change continually with the rudder changes! This often led the trainee to suspect, when in the sim. that "sir" had tweeked up the wind without telling. Not so, just poor rudder use. I occasionally used to demo this on the downwind leg at low speeds.