Jumpstreet - murder is nonsensical in and of itself. Murderers are nonsensical as well.
Refering back - I have no idea what LE knew or what they were thinking. The response to a reporter concerning a POI or suspect could have and probably should have been that they were treating it as a missing persons case - end of sentence. Regardless of what they may have thought they still had a duty to search for Nancy until the search was exhausted.
LE typically talks about suspects or POIs when dealing with a missing persons case that involves a KNOWN abduction. If that is known - they will issue a description of the POI if they have a witness or something to point to the person. If a vehicle has been used - if LE has information they do issue a description of the vehicle if they have it.
I find it odd they were even responding to the issue of a POI or suspect since Nancy was not reported to have been abducted. Odd wording perhaps, definitely odd to me.