The opposite is true. Here some references:
Psychopathy and narcissistic personality disorder are two completely different things.
Narcissists operate from the assumption that they are perfect and absolutely wonderful at everything they do; as a result, they very rarely become good at anything. Because, in order to become good at something, you have to have an understanding that you are not good at it now—and a narcissist will never admit, even to him/herself, that he/she is less than perfect. Narcissists interact with other people in order to manipulate the other people into confirming how great they are; they are so consumed with themselves that they do not see other people as individuals.
A psychopath is someone who cannot empathize with other people. He or she usually does see that other people have emotions, and often, psychopaths become quite adept at manipulating those emotions. They don’t internally reflect the emotions that they see in other people (although many psychopaths can mimic that ability). Psychopaths can be very successful, because the unpleasant aspects of becoming successful are not unpleasant for them. For instance, as a supervisor, I have to sometimes tell employees that they need to change their behavior, and I am quite aware of their upset/anger when I do so. So I am hesitant to tell them, and only can force myself to do so because I know that the situation will only get worse if I don’t say anything. A psychopath would have no trouble, because a psychopath is focused on the end result, not the person’s feelings.