When the FBI gets involved in cases do they take the lead or just help alongside the local detectives? Do they withhold any information? Do the local detectives on the case share info with other officers or do they keep it secret? Does anyone know how it works?
Here is my theory about the sketch, all JMO.
Abby mentioned to LE that the guy was called Kibby and she described things about him like guns, politics, survivalist training, hunting, lived in NH, etc. If she mentioned this then maybe it simply was not shared with the police who gave Kibby his gun back.
IMO the detectives took the name and other info from Abby and did their OWN Internet sleuthing, similar to what we did here, and they discovered a guy called Kibby (or at least that was his online username n forums and such) who had the exact same interests as NK. They found images of this man online among all of his many forum posts and they copied his features and made their OWN sketch.
This 'other Kibby' had a very extensive online presence and AFAIK NK has zero online presence. They then jumped the gun and thought they had the right guy, when in fact it was just a crazy coincidence.
IMO I think Abby saw the sketch and questioned it because it was clearly not a sketch of NK. Maybe then she convinced them that they were sleuthing the wrong guy and in that 48 hours time they realized, oops! wrong Kibby!