The Nazis did capture at least two P-47s but it is very unlikely they ever flew them together in combat missions. (They often repainted the tails in yellow to identify them as captured machines.) More likely this incident was blue-on-blue. Recently read an account of the Rhine crossing which describes a similar event - and in this instance ground forces returned fire and brought down one of their own attacking ‘planes.
You're probably right about friendly fire but when adrenalin was up a FW190 could look a lot like a Jug.