Do all people with narcissistic personality disorder really have low self esteem?

Absolutely not.: There are probably some types of narcissistic personality disorder that are based on trauma. In those cases i would agree that the core problem maybe low self-esteem secondary to trauma. However, for those people are born with a narcissistic temperament, they do not have trouble with low self-esteem, rather, they have a primary deficit in empathy.

Low esteen: Can be opposites. Narcissism can have inflated self-esteem and love of self.

Narcissism: The hallmark of a narcissist is an immense ego, grandiosity, and self-importance, as well as being entitled, and a tendency to use and objectify others as well as thinking of people in all-good or all-bad terms instead of shades of gray. The core of a narcissist is profound insecurity.