Did the Luftwaffe use captured Allied Aircraft as 'bogies' & 'spotter aircraft' frequently in the defence of the Reich?

[F for Freddie]

Did the Luftwaffe frequently use captured Allied Aircraft as 'bogies' & 'spotter aircraft' in the defence of the Reich against the US Bomber formations and their escort fighters?
I am quite new to this forum, but fascinated by this little known possibility. But having read US VIIIth Fighter Command Narratives of Reports based on late 1943. It appears that Pilots including as high as US Flight Colonels reports suggest this is a possibility. They often are reported (generally 'unnumbered') 'old marked' P-38s and P47s engaging in dogfights with their own planes. In one case a unusual marked B24 was reported even observing from distance a 'box' B24s & B17s formation and acting oddly though not in distress.
I know in the heat of battle, friendly fire was common and mistaken identity could be easily done. However the frequency of the Reports and sometimes the detailed descriptions suggest these are not mistaken identity?.
Does any one have any good examples of this they can share?