True, but that still doesn't effect the flash light hitting the subject, it effects the ambient light. I never said that shutter speed doesn't effect the ambient. I actually said:
I was clarifying your post, because while it doesn't effect the flash hitting the subject shutter speed up to max sync (including high speed synch on flash/body combos that allow it) really doesn't matter if you're not dealing with a huge amount of ambient light, but shutter speed totally matters in terms of flash to ambient ratios. Most beginners don't really get that and they live totally at max sync speed for years.
If I were nitpicking, then I'd have taken exception with
Using flash allows you to expand the range of light your camera will record, because you can expose for the darker areas, and fill in where you want with flash.
Because flash most certainly
doesn't change the range of light the camera can record, that's
fixed by the dynamic range of the sensor, it changes the dynamic range in parts of the
scene by bringing up the light level in those parts.
For completeness, technically, shutter speed over the max sync speed does have an effect on flash- or at least the camera's ability to record it- if you're going to be ultra-picky, shutter speed doesn't have an effect on any lighting- ambient, natural, flash, artificial or any combination thereof- it has an effect on exposure- however I was clarifying based upon the intent of the statement, not it's absolute meaning which would have been moot if we were being that picky.