The ultra light situation is a special case. If we look at a representation of pressure distributions on a generic asymetrical airfoil under various conditions it can possibly illuminate the discussion.
The first picture illustrates pressures on various parts of the foil and is helpful in visualizing whence the negative pitch moment arises:
As a matter of convenience we can resolve the forces acting on the wing as a single lift vector and negative moment around the
aerodynamic center Moment is just another word for torque. A negative moment is counter clockwise and assumes that we are looking at the left side of the foil. This equates to pitch down:
In the following sequence we can watch the change in pressure distribution from zero lift (-3 degrees AoA for this foil)
Through a typical cruise AoA:
To somewhere in the vicinity of CL Max:

Correction: The aerodynamic center is the theoretical point at which the wing responds to the moments acting upon it. It does not move with changes in AoA. The Center of Pressure is what is moving.
Although the Cp is not depicted you can see some things happening as we approach CL Max. One thing is that the Cp is moving forward. Under certain conditions it might be possible for the Cp to actually overtake the CG. Although we are looking at the wing in isolation this would be the Cp of the system.
It is therefore possible to lose the tail and have the aircraft pitch up. As HiTech said (and I agree) the CG merely has to be behind the Cp of the system.
If you do the balsa glider experiment it will pitch down if you throw it normally however if you keep launching it at progressivly higher angles of attack you can eventually get it to pitch up. Keep in mind that it would be hard to describe the airfoil on a balsa glider as asymetrical and you are entering the land of flat plate theory where I don't tread.
However, my earlier statement: "When the horizontal stabilizer departs a normally loaded conventional aircraft in the normal flight envelope it pitches down violently etc." is valid unless you consider angles of attack approaching Cl max as part of the normal flight envelope. You can't get the aircraft to anywhere near Cl max at speeds appreciably in excess of Va without waving goodbye to an important part of the aircraft structure. If you get the thing slow and greasy and yank back on the stick just before smacking a wire all bets are off.
I guess I flinch when HiTech says "Planes can be perfectly stable with the horizontal stab producing up or down force." While technically correct I can't think of an instance where there is not neutral to downforce at the tail in unaccelerated cruise flight. Flying an airplane around with the tail holding you up is possible but not a good idea.
Several years ago we were giving glider rides to Boy Scouts. I had several chunky scouts and the last scout of the day was a little tiny scout. I was too lazy to walk across to get the 25 pound ballast bar that was supposed to be installed for small people. The tail of the glider (SGS-233) would not come up during the takeoff roll and about the time I was reaching for the release to abort we became airborne. Once we had enough airspeed things were peachy it was in fact "perfectly stable". The landing was interesting in that as we bled speed in the flare I had to apply progressive forward stick and had it maxed out to the stop at touchdown. Needless to say that flying any slower would have resulted in an unrecoverable pitch up followed by a probably unrecoverable stall followed by waking up in a tube of light with the tiny scout and Elvis.
Apologies for the length of this post. I'm going to find something constructive to do with my time. Honest.