IIRC the first Boeing view is more likely. Residual fluids are believed to reduce the aircraft climb performance, thus it would be poor practice to allow a reduced performance take off where a further reduction is possible.
Another thought is that where de-icing is used widely, then the fluid departs the wing during take off, with the majority being shed at rotation. The fluid remains on the runway just where max braking might be required in the event of an RTO. A full power take off would enable a larger safety margin.