Do you know what a pitching moment is? And, a horizontal stabilizer is a LIFT surface, regardless of whether it is in front (as a canard) or in back.
The fact that it is lifting surface does not mean that lift must be directed *up*.
1. Most normally-configured aircraft have center of gravity ahead of their center of lift. This is considered vital for positive stability, and having a center of gravity aft of the center of lift is considered positively dangerous.
2. Most "normal" airfoils have a negative coefficient of moment. In plain English, their tendency is to actually want to pitch downwards. In this case, it follows then that the horizontal stab of an aircraft which is normally configured must actually generating *down* force to hold the nose *up*.
3. Thus the OP's surprise at aircraft pitching nose-up when they suddenly loose the horizontal stab is understandable...IF we assume the planes modeled in AHII have a CoG ahead of the center of lift AND we assume that the airfoils have negative coefficient of moment.
EDIT: Stoney, whether flaps increase nose-up or nose down pitching tendency has alot to do with the airfoil. Airfoils with a high and negative coefficient of moment tend to pitch down with flaps, while airfoils with a low coefficient of moment may tend to pitch up. Laminar flow airfoils tend to have a high and negative coefficient of moment.