The meaning of the Prime Directive shifted a bit over the years. Back in the day, TOS never suggested that the PD meant that you had to stand by and let a people get wiped out by natural disasters. (See "The Paradise Syndrome.") It just meant that Starfleet personnel weren't supposed to meddle with the historical development of other cultures by, say, turning them into Nazis or teaching them how to use gunpowder. (Oops!)
Later Trek shows sometimes took the PD to ridiculous extremes (See "Homeward"), but what I got from the new movie was that the issue was revealing themselves to the natives, not saving them from the volcano.