It seems to me that if you submit the serial number to the police that would be proof enough, how could you have the serial number if the gun wasn't yours or in your possession? Plus, you're the guy that reported it stolen and that is on file otherwise the police wouldn't have called you to pick up the gun.
In the not too distant past unsuspecting individuals would post pictures of their guns on gun forums without covering the SN#. Anyone on the internet could see the SN# and report it stolen. Then just sit back and wait.
Did that ever happen? I don’t know. But the point is someone else could have the SN# and report it stolen.