Joey:
A KWHr recorder is not cheap. I have one, and I think it was $7-900, when I bought it.
That said, from experience, utility meters (POCO's) are accurate! Here in NJ, the Board of Public Utilities (go figure), a Govt agency regulates the POCO's, and has stringent tolerances for metering & billing. You also could request the POCO to check the meter.
That said, it could boil down that the person complaining about the bill just that....complaining. BTW, have you had any rate increases (KWHr or others)
John