I see this happening far too often to make that statement true:
Badlands - first time director, first time DP
Blood Simple - first time directors, first time DP
Slacker - first time director, second time DP
Boyz N the Hood - first time director, second time DP
Mallrats - first time director, first time DP (not counting Clerks)
Reservoir Dogs - first time director, first time DP
Eve’s Bayou - first time director, second time DP
Buffalo ’66 - first time director, first time DP
American History X, first time director and DP
Girlfight - first time director, first time DP
Being John Malkovich - first time director, second time DP
Wolf Creek - first time director, first time DP
Layer Cake - first time director, second time DP
Spun - first time director first time DP
Napoleon Dynamite - first time director, first time DP
Half Nelson - first time director, second time DP
Frozen River - first time director, second time DP
Moon - first time director, first time DP
Quid Pro QUo - first time director, second time DP
District 9 - first time director, first time DP
Sound of my Voice - first time director, second time DP
Attack the Block - first time director, first time DP
Beasts of the Southern Wild - first time director, first time DP
Palo Alto - first time director, second time DP