Fudge's account of these events in chapter 10 of Harry Potter and the Prisoner of Azkaban is quite clear (emphasis mine)
“Pettigrew died a hero’s death. Eyewitnesses — Muggles, of course, we wiped their memories later — told us how Pettigrew cornered Black. They say he was sobbing, ‘Lily and James, Sirius! How could you?’ And then he went for his wand. Well, of course, Black was quicker. Blew Pettigrew to smithereens. ...”
But later on, in chapter 19 Black claims:
“When I cornered him, he yelled for the whole street to hear that I’d betrayed Lily and James. Then, before I could curse him, he blew apart the street with the wand behind his back, killed everyone within twenty feet of himself — and sped down into the sewer with the other rats. ...”
Isn't this a contradiction? As far as I can tell, with his wand behind his back, he's managed to make an explosion, cut a finger off, and transform in to a rat. That's already impressive, but he's also managed to do this with the (admittedly muggle) eye-witnesses thinking not only that nothing strange has been done by Pettigrew, but that he was reaching for his wand. How did Pettigrew pull this off?