Loss of airspeed would result in a higher rate of turn...
It’s a bold move to attempt to correct someone offering the benefit of their experience with a statement that belies so little knowledge, especially when that person is a combat-experienced Harrier pilot! Your quote above is only true at a fixed bank angle at zero pitch rate above stalling speed; you might consider taking some elementary training in steep turning. In combat, turning is achieved by rolling to point the lift vector in the desired direction and pulling to attain maximum lift (and therefore turning performance). Maximum attainable turn rate rises with airspeed until Vc or ‘corner speed’ because the increase in available lift (a factor of V-squared and part of the numerator in a turn rate equation) dominates the calculation (in which the denominator is a factor of V). Turn rate decreases above Vc as structural load limits prevent additional lift from being applied.