Don't think this progression is strictly diatonic. If key of D, C and E are borrowed. If A, G and C are borrowed. If G, A and E are borrowed. If C, A, D, E are borrowed etc. Seems like a V - IV - I prog in D for the intro. (Haven't actually listened to the song.) C is borrowed- bVII And E is V of V. Seems like D is the simplest explanation to me personally. Could also be in A, with a bVII and bIII chord. Either way I would have to hear the actual song to see the timing and rhythms to get a clear sense.