Recent reports on the production of hydrogen peroxide (H$_2$O$_2$) on the surface of condensed water microdroplets without the addition of catalysts or additives have sparked significant interest. The underlying mechanism is speculated to be ultrahigh electric fields at the air-water interface; smaller droplets present higher interfacial area and produce higher (detectable) H$_2$O$_2$ yields. Herein, we present an alternative explanation for these experimental observations. We compare H$_2$O$_2$ production in water microdroplets condensed from vapor produced via (i) heating water to 50-70 {deg}C and (ii) ultrasonic humidification (as exploited in the original report). Water microdroplets condensed after heating do not show any enhancement in the H$_2$O$_2$ level in comparison to the bulk water, regardless of droplet size or the substrate wettability. In contrast, those condensed after ultrasonic humidification produce significantly higher H$_2$O$_2$ quantities. We conclude that the ultrasonication of water contributes to the H$_2$O$_2$ production, not droplet interfacial effects.