Koyovis' explanation is correct and deserves to be the accepted answer. However, as always, much depends on the details of the specific configuration - generalizations like those in your question deserve to be treated with some caution.
Ground effect does not always result in a pitch-down change. The Handley-Page Victor was famous for its ability to flare all by itself when entering ground effect. From Wikipedia:
One unusual flight characteristic of the early Victor was its
self-landing capability; once lined up with the runway, the aircraft
would naturally flare as the wing entered into ground effect while the
tail continued to sink, giving a cushioned landing without any command
or intervention by the pilot.
The key factors were the T-tail and the low crescent wing: Since the wing would enter ground effect much earlier than the tail surface, its lift would increase earlier. The low wing in combination with the high tail would add a pitch-up change in ground effect.
Why is the lift curve slope different in ground effect? The proximity of the ground reduces not only the downwash angle but also the induced angle ahead of the wing. A highly cambered wing with low angle of attack will experience a reduction in lift. However, with a positive angle of attack the airflow below the wing will be partially blocked by the ground, so pressure will increase below the wing and force more air to flow around the leading edge and over the wing, resulting in an increase of the lift curve slope.
With a low tail, the handbook is correct, however: Since the tail flies in the downwash of the wing, a reduced downwash results in a positive angle of attack change at the tail, increasing lift there and resulting in a pitch-down change. This comes on top of the change in the pressure distribution over the wing which shifts the center of pressure backwards, adding more nose-down pitch, as described by Koyovis. Leaving ground effect will lower the angle of attack at the tail and makes itself felt as a pitch-up change.
The F/A-18 has suffered from this effect and needed a kludge to restore its pitch control power to the out-of-ground-effect value, namely toed-in rudders. As Jan Roskam explains in his book "Roskam's Airplane War Stories" (War story 108):
When the first F-18 fighter […] was flight tested at Patuxent River,
it became evident that the airplane would not rotate at the predicted
speed. This made the field performance of the airplane unacceptable.
The problem was traced to an error in the calculation of aerodynamic
forces in ground effect. This is particularly severe in case of a low
placed horizontal stabilizer. As a result there was insufficient
down-load capability to effect early rotation during the takeoff
The problem was fixed by toe-in of the rudders. A squat-switch on the
main gear biasses the rudders to deflect inward while on the ground.
This creates enough positive pressure over the aft fuselage to effect
This fix, although impressive, came at a price. All flight control
software had to be revalidated. Also, the squat-switches represented
additional system complexity.