There are several different factors going on with optics, physic of lighting, electronics and optics.
Video is not more accurate, inherently. Mirror quality is often made cheaply and distorted.
Firstly, as was just stated, mirrors often have optical distortions. Sometimes more than one mirror in comparison might have more than a few distortions. Mainly, those distortions may not be flattering. You're just becoming aware and noticing this.
Secondly, cameras and lenses are better at capturing people depending on the focal lenths. and quality of optics. Also, as you're record your image using certain lighting, you will edit and favor the better lighting. you capture that better moment in time. Whereas a mirror captures an ever-changing lighting, angle of posing, and a moving target.
Generally, when you record with the camera, you'll edit ones that are more flattering and eliminate the less flattering.
The mirror is designed for a different much less critical purpose than a camera and lens combination.