With regard to what was and what was not taught regarding flight control application ... we'll probably not know for sure whether or not a specific comment was made or a specific reference was included regarding "control reversals" ... specifically "rudder reversals," for any specific airline training program. But I can say, rather confidently, that the AA "Advanced Airplane Maneuver Training" materials talked specifically about rudder application using the reference of maintaining "coordinated flight." The last time I looked, that meant keeping the inclinometer index centered ("the ball in the middle"). To my knowledge and throughout my career, there never was any instruction to "rapidly reverse" ANY control application ... and, again, to my knowledge, the only thing that even approached this condition was the recovery from the infamous "Dutch roll." As anyone who ever was required to see and recover from this infamous condition in the airplane can confirm, the procedure was to first "center the rudder pedals and maintain that position," then apply up to full aileron control opposite to the direction of roll as the wings passed through the level flight position and then immediately return the aileron control to the neutral position and freeze it there. If the roll reversed and exceed wings level, the aileron control was again to be used, up to full input opposite the roll direction, and, again, immediately return the aileron control to the neutral position and freeze it there. This procedure was to continue until the Dutch roll was arrested. Why? This was deemed to be the appropriate control application to recover from the condition. And, as anyone familiar with flight test techniques can confirm, full control application at speeds below design maneuvering speed is allowed provided the controls are immediately returned to the neutral position. Sound familiar? And, one would be well-reminded about the surfaces involved and the differences between the aileron surface and maximum deflection versus the rudder surface and maximum deflection.