DoP specializing in Sports Cinematography.
I believe we're having a heated agreement. Your last line sums up the point.
A bit of misinformation here. Changing your frame rate absolutely affects your exposure with a digital camera. The frames have less time to expose so the exposure on each frame is reduced. The result from shooting an image at 120fps vs 24fps - shutter speed held constant - is a reduction in exposure of the image. Shooting with a phantom camera at 1000 fps requires an enormous amount of light for this reason - not because the shutter speed changes.