There is a reason I said that my statements apply for the LINEAR range. This means small angles. By taking the example to extreme dihedral angles and extreme angles of attack you have invalidated one of the many assumptions used in typical aircraft stability and control calculations. I agree with you that if you had a wing with a huge anhedral angle, it would be destabilizing longitudinally. However, for reasonable angles (<10 degrees) the dihedral/anhedral angle has VIRTUALLY no effect and can be ignored.

One of the first assumptions made when calculating the aircraft pitching moment coefficient with respect to angle of attack is that the angle of attack is small such that sin(alpha) = 0 and cos(alpha) = 1. If you work out the equations, the change in wing aerodynamic center of a wing with dihedral is:

dx_ac = y_ac*TAN(DIHEDRAL)*SIN(ALPHA)

Therefore, according to the small angle assumption, this change is negligible.

There are many higher order factors affecting stability calculations that are ignored. The important thing is to keep the primary factors in mind. Maybe I shouldn't make such bold, definitive statements, but if someone ever said "Dihedral affects longitudinal stability" in one of my design reviews I'd throw them out of my office.

If you want to include every higher order term you can in your stability calculations, go ahead. I'll take my +/-5% accuracy and move on.