Because it's information that only someone with intimate knowledge of the crime would know. So if someone confessed and said, "here's what I did" or slipped up during interrogation and eluded to a method of death, LE would know they had the right person. They also would find it harder to know--if they released too many details--if a possible confession was true, as false confessions do happen. If someone came forward saying, "this guy I was sleeping with got angry with me and said, 'I'll [insert means of death] to you, just like I did to Morgan", LE would know whether the guy in question was BSing or might be the perp.
It's something they have to think about when releasing any information. I get frustrated sometimes after the fact when I find out how much LE know and some of the things they didn't released would have led to the perp sooner. But sometimes, it's the things they don't release that allows them to capture the perp of a crime.
In the case of COD, I don't know if that would lead to useful leads. Saying the person had access to guns would probably not narrow leads down as, if Virginia is anything like West Virginia was when I lived there...well, more people have access to guns than those that don't. And other methods of killing really wouldn't offer many clues, IMO.