The phrase "perverse sense" means having a twisted or abnormal way of thinking or feeling. It refers to a behavior, belief, or action that goes against what is considered normal or reasonable. Full definition
I've come to think he has a nicely perverse sense of humor, and chooses them for that reason. (writerunboxed.com)
(Well, I take that back, it makes perverse sense. (alephblog.com)
The viewer is perhaps meant to drop their jaw at seeing this attractive woman stuck on a contained boor such as Vincent, but her reason, which she lets on late in the movie, makes perfect if perverse sense. (rogerebert.com)