Not quite correct: most often, the wires are wound in the same direction, but on opposite sides of a single core, maximizing leakage inductance while still getting current cancellation. Using two independent cores, however, will probably saturate them, because the currents are unbalanced (instead of ferrite, powdered iron cores would be required, and the inductance will be much lower). The same is true if you screw up the direction of one wire -- the currents add rather than cancel, the core saturates, and you get little effect.
I'm curious how one could "screw up" a nixie clock such that it trashes the 2.45GHz band! I wonder, does it matter how close in proximity they are, or if they are plugged into the same outlets? If it is interference, I would be surprised if it's going up the power line; it's probably radiating from something internal, which means a careful inspection of the circuit layout and what kinds of things could be causing it.
Tim