Many years ago I had something similiar happen, except they thought my truck was involved in a hit and run. My truck was blue, but they were looking for a red one same year and model, same license plate. Ran the plate and got my address, and came to pay me a visit.
They passed my truck in the parkng lot of the complex, but either they didn't see it or just wanted to triple check. After they said my plate had been reported in a hit and run with another vehicle, I thought, "Oh shit! Someone stole my license plate!" So I asked them could we go down and look they said sure.
1995 Ford F-150. Check
License plate number, Check and was still there.
But they wanted a red one and mine was blue. After they walked around the truck they said, well, wrong color and no damage, so obviously someone got the wrong plate number. Have a nice day, sir.
Not the same as your story, but close - sans the color. I don't think they would have been so convinced they just had the wrong color except there was no damage on my truck and the one they were looking for was pretty messed up from the accident, given what they told me (6 car accident, and that vehicle was involved, and then crashed into another vehicle fleeing the scene).
Wierd.