I don’t think they can prove that.
Actually, one can prove for certain that Brown did not get the kill. That doesn't diminish his valor at all, but it wasn't his kill. The wound that killed Richtofen would have killed him long before he landed if it had been inflicted by Brown's machine guns, and the angle is problematic. If Brown had fired the fatal shot Richtofen would have fallen out of the sky instead of landing his bird. Plus, the entry angle matches where he was when the Ausies opened up on him.