Actually the field from the top conductor adds to the one from the bottom in the area between the conductors. The reason the inductance decreases when the gap reduces is that the area reduces, hence the flux linkage reduces.The inductance goes down as the plates become closer together because the magnetic field, caused by the current in the top conductor, is better canceled by the magnetic field from the current (going in the opposite direction) in the bottom conductor. It's the changing magnetic field around a conductor carrying an AC current that causes the inductance. The more this field is canceled, the lower the inductance.
It is said there that a straight wire has an inductance, but as far as i know, magnetic field is not enough to create inductance, but a magnetic flux thourgh a closed area is.