It is ABSOLUTELY a narcissistic trait. It is, in some books on the subject literally called "crazy-making". They extract what they want to hear from something you said and interpret it to their manipulative advantage. The latest type I have been dealing with is the "paranoid" interpretation, where something I've said has been interpreted as a direct attack to my N mother. Or, perhaps, you mean you say one thing, and they "repeat" it back to you, except it is completely different than what you actually said. One of our regular posters, Rob, appropriately has termed this "word twisting".
Don't worry, you are not crazy. You said what you said, and you heard what you heard. Don't argue with them, just know it in your heart. Diffuse it the best you can by not validating their misinterpretation. Ignore, ignore, ignore. Very much easier said than done, I struggle all the time. Your defense mechanism is to deny, argue and defend. But the truth is, the less you acknowledge the crazy making, the less tendency the N has to be a repeat offender. When they see it is not effective, they stop using the tactic.