There very well could be truth to the story I know for a fact that the Luftwaffe used captured examples of Allied aircraft against the USAAF and RAF. On 4 March, 1944 Lt.Albert Fogg, 79thFS/20thFG was nursing a damaged P-38 home when attacked by an unmarked P-47...
"Believing the plane was also damaged, Fogg slowed down to allow him on his wing. Instead the unmarked P-47 came at him with all eight guns firing. Not sure if the pilot was an American who needed more time looking through recognition manuals or a German pilot flying a captured aircraft, he managed to evade him.
"Even though he was only flying with one engine Fogg dove and made a pass toward the P-47 hoping it would drive the pilot off, but he was persistent and managed to hit the P-38 several times. Both the plane’s turbo-regulator and its good engine began to act up so Fogg made one more pass and managed to drive his attacker off.
"Fogg survived the subsequent crash landing and returned to action soon thereafter. He eventually was shot down and became a POW at Stalag III."
This is just one example. The Luftwaffe actually had a special opertaions battle wing, KG 200 which used numerous captured Allied aircraft for various purposes.
For more try:
http://www.warbirdsresourcegroup.org/LRG/foreign.html
http://www.stahlbrandt.com/html/history/kg200.html
also Google the terms KG 200 and Kampfgeschwader 200