Framer
I think you may have mis-read the book or are reading from the landing section where you increase aileron deflection as the speed decreases and the ailerons become less effective.
I find it hard to believe that Boeing would publish something like this. If you start at neutral and work into the wind as the airspeed increases you're trying to roll the airplane while it's still on the ground. This puts extra stresses on the landing gear and really stresses that work their way back to the wing root. Not to mention differential drag on the main landing gear causing a yaw in the direction of aileron deflection. So that takes care of the problems on the ground.
Now for the problems in the air. The ailerons work by changing the lift on the individual wings. Aileron down, increased angle of attack, more lift and vice versa. So as you get closer to Vr one wing will be making the lift required for rotation before the other. You can see where this is going. Now you have one wing flying and the other one...well...not. And since both wings are connected, with asymmetrical lift one goes up, the other goes down. And it's not long till the tip of the wing meets concrete and the insurance rate begins to climb.
The procedure for takeoff (this could be different in the bigger jets with roll spoilers and all that stuff, the biggest thing I've ever flown is a King Air) is to start with the ailerons deflected fully into the crosswind, whether it's a headwind, or tailwind, that doesn't matter, because like someone else said the tailwind is gone by the time the engine is halfway to takeoff power. As the airspeed increases you'll feel the control forces increase (hydraulic controls too? I think, dunno, never flown 'em) so you slowly "give in" to the suggestion the airplane is giving you and begin to return the control wheel to neutral. The goal should be to hit neutral just before rotation speed, pull the airplane off the runway, and adjust bank angle as appropriate.