As far as I know, it's just a Las Vegas thing, and has nothing to do with Clark County. Maybe someone in Henderson or Boulder City can clarify it.
I know that in 1999, I didn't go through with a purchase in Las Vegas because of the waiting period. I went to Henderson and bought the pistol the same day.
The funny thing is that when I purchased the pistol in Henderson, they issued me a blue card. I could have gone back to Las Vegas and purchased another firearm the same day.