In California, first-degree murder, or murder one, requires the prosecution to prove and the jury to find, that the defendant acted "willfully, deliberately, and with premeditation." The key word here is "willfully." Willfully in this context is explicitly defined as an intent to kill.
Jurors considering a first-degree murder charge are instructed, "The defendant acted willfully if he intended to kill." Thus, to convict someone of first-degree murder absolutely requires an intent to kill.
Nancy Grace may have been thinking of the requirements for second-degree murder. Second-degree murder in California can be found with either an intent to kill or intentionally doing an act with a conscious disregard for human life. This is a state of mind called implied malice, which I discussed a couple days ago.
Although my opinion on the propriety of charging Dr. Murray with murder differs from Nancy Grace's, I am more concerned with making sure people know the truth about our laws.