Lightmeters are superior to in camera metering because they are able to measure the incident light, not just the light reflected off the subject.

Reflected light metering is less accurate as the camera/meter has no way of telling the difference between a white cat that is massively underexposed and a black cat that is correctly exposed.

With incident light metering you are not trying to detect hotspots on the subject that could be overexposed, but instead you trying to measure the strength of the light that's about to hit the subject (before it bounces off toward the camera). If you know how strong that light is then you can be sure that no part of the subject will be overexposed, even if they move.

If you just try and measure the reflected light from the brightest part of the face then you could get overexposure if the subject moves and another part of the face reflects even more of the incident light.

For it to be accurate you need to hold the lightmeter somewhere close to your subject, with a direct line of sight to the lightsources, but also somewhere that isn't reflecting a ton of light back onto the meter (most meters have a single hemispherical collection surface, so light from the subject is generally not a problem).

This may have been why you've seen videos of lightmeters placed under the chin, it's a convenient place to hold the meter that is close enough to be accurate, although in my experience in front of the cheek is more common. It is possible, though unlikely, that the meter was set to record reflected light from a shadow region in order to judge the strength of fill light needed, in this case you'll see the white dome has been removed.