Not true - there are many, many documented cases where individuals have been shot in the heart and not died until they bled out. In fact, a female LAPD officer was shot point blank in the heart with a .357 magnum during a home invasion and struggled with her attackers until she fought them off. She survived to tell about it.The human body has only a few areas where an injury causes sudden death: the heart...
In the Dallas area a LEO struggled with a suspect and during the fight the officer shot the suspect in the heart. Before the suspect bled out from his injuries he continued to fight with the officer, take his weapon away and kill him. We were (and still are) taught that the only instantly incapacitating shot is to the cerebellum, a part of the brain that controls voluntary movement that lies at the base of the skull. During sniper training we would fire at targets that had a dot placed directly below the nose and right above the top lip to indicate where we needed to aim to hit that area.