Nose down trim
alatriste,
I don't know much about the A320, nor am I an aeronautical engineer. However, with that in mind, I may be able to help with your question.
An aircraft may still be longitudinally stable as long as the horizontal stabiliser is operating at a lower coefficient of lift than the wing. Thus, some aircraft may use nose down trim and still be stable - as long as the trim is only slightly nose down!
I'm cautious with my answer because it does depend very much on the CL characteristics of both the wing and the stabiliser.
For example:
=> of the wing and the stabiliser, which has the steeper CL / AoA curve, and which has the greater critical AoA?
=> as you've commented, the stabiliser may be cambered or not, affecting lift and therefore stability at a given pitch setting.
=> the shape of the fuselage affects aircraft stability - usually fuselages of circular cross section are unstable in pitch.
Awaiting experts' corrections,
cheers,
O8