Yes, a possessing demon has the capacity for subtlety. Except when it comes face-to-face with another who is not demon possessed but more than that, carries the Holy Spirit within.
The demon in the possessed completely LOSES HIS SHIT when that happens. Remember in the Book when the demon within the possessed man met Jesus. He screamed: 'What do you have with me, screeched: let me alone.
So Jesus did as the demon requested. The demon was released from the man and entered a flock of sheep.