Normally, a fast skimmer can shoot if it moves up to 12". If it moves up to 6", it can shoot all it's weapons. If it moves more than 6", and up to 12", it can shoot 1 weapon (plus all defensive weapons).
When you go Flat Out (which is more than 12", and up to 24"), that is when you get your cover save.
I don't have my BRB in front of me right now, but I'm pretty sure that's how it works.