I'm not sure I understand how they had voltages on either "leg" when the open neutral effectively eliminates the "legs."
However, a higher than normal resistance on the neutral leg, such as a bad connection, would serve to waste consumption, meaning the customer would be paying for watts used without any benefit.
In my experience, when the voltage on either "leg" decreases with increased load, it indicates line losses, either from the meter to the pole or from the meter to the panel. I just looked into a customer complaint of some of his lights dimming when he turned on a shop vac. Turns out, his house is at the end of about 200+ feet of wire from the transformer to the meter. Pretty much can't do anything about it except eliminate any wiring problems on his side of the meter.
Loosing the system neutral conductor can indeed result in a higher kw reading on the meter, depending on how the grounding/ plumbing is done in the area. Grounded metal water pipe that is continuous to the other houses on the same particular utility transformer can become your "neutral" in those circumstances, via the other houses service as a path back to the utility transformer for the neutral current. Depending on the impedance of that path, it affects the consumption. Not a healthy setup for plumbers either.
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