[Ghoulish Delight]

Not entirely accurate. Some rules have specific definitions. For example, the definition of offside is when an offensive player goes past all defensive players (except for the keeper) before the ball does (there's more detail than that in the full definition, but that's a mostly accurate summary). There should technically be no room for "interpretation" or "leeway" on that, either you're offside or you're not. Of course, it comes down to whether the refs see it accurately (or are being paid off).

But yes, there are other things that are less precisely defined, mostly revolving around physical contact. You're allowed physical contact as long as it's not dangerous and doesn't give you an unfair advantage. And the lines there are left up to the refs to draw. And no, they don't have to identify a specific penalty that's being called.