Of course, there are two kinds of perversity.

Perversity is "a deliberate desire to behave in an unreasonable or unacceptable way; contrariness."

Fictional genies seek out ways to trick the requester on purpose, just to prove a point about rash wishes. The other kind of perverse agent doesn't act contrarily for the sake of being contrary. They act exactly to achieve the goal and nothing else; it's just that they go against implicit goals as a side effect.