The DF circuit is fine If the transistor was an NPN as the LCD backlight doesn't need more than 4 volts to work properly, The emitter follower actually is a blessing there as full 5V isn't required. a PNP connected properly (Emitter more positive than collector and emitter and the base -.6 V with respect to the emitter you have a full on high current switch. I do agree though it is more likely the mistake of the draftsman or engineer who did the drawing because it either is the wrong symbol or miswired.
Bob