Sine Wave Inverter Anomaly

Does the fan even have a connection to the ground wire? Assuming it has a 2-prong plug and no ground connection, how could it be affected by voltages it doesn't have access to? As to the squeal, almost all pure sine wave inverters build the waveform with high voltage pulses of varying lengths (Pulse Width Modulation, or PWM). This creates a horrible-looking waveform that, with some filtering, closely resembles a sine wave. The "closely" qualification means that there is a small higher-frequency signal riding on the sine wave, equal to the frequency of the pulses uses to build the sine wave. The quality of the filtering varies from inverter to inverter, possibly related to "you get what you pay for". The pulse frequency is likely somewhere between 15 kHz and 25 kHz, and it sounds like your fan is reacting to it. I'm a bit surprised by this.