Given the Nazi propensity for Lying, and that the effects of Mach-1+ travel were known before the actual event (wind tunnels, etc.), it's more likely this was an attempt at propaganda, and/or misinformation ("let the word spread that we have a fighter which can travel over 200 MPH faster than anything the enemy has; maybe then, they'll back off"; but then, Adolf's bunch were never known for their solid grip on Reality).
Like folks say on the 'Net: "Pictures, or it didn't happen."
After Willy Messerschmitt's death, the former Me 262 pilot Hans Guido Mutke claimed to be the first person to exceed Mach 1, on 9 April 1945 in a Me 262 in a "straight-down" 90° dive. This claim is disputed because it is only based on Mutke's memory of the incident, which recalls effects other Me 262 pilots observed below the speed of sound at high indicated airspeed, but with no altitude reading required to determine the actual speed. Furthermore, the pitot tube used to measure airspeed in aircraft can give falsely elevated readings as the pressure builds up inside the tube at high speeds. From Wikipedia.
"The airspeed indicator was stuck in the red danger zone, which is over 1100 km/hr.
I noticed that rivets began popping out of the tops of the wings.
The airplane began vibrating and shaking wildly, banging my head against the sides of the cockpit.
After diving about three miles I again regained control and was able to return to base.
On the runway the mechanics were very surprised by the appearance of the airplane, which looked as though it had been shaken by the hand of a giant."
www.vho.org/tr/2003/1/Chelain69-71.html Here is a page discussing it. True or not true, this is not a nazi propaganda thing and as I said: It is possible. And it is something that are still being discussed by engineers right now. it may or may not have happened but don't just think that the pilot was a nazi so it can't be true.