For a bunch of good reasons, I suspect

* Dispatcher is a 911 dispatcher, not a trained law/law enforcement person. She may not know the law, or even if she does, feel comfortable dispensing legal advice.
* Dispatcher was in the moment, the detective was answering a reporters question in the aftermath
* Dispatcher is in a position where incorrect advice could land the caller and possibly a mistaken dispatcher in a pile of trouble. Detective can say just about anything to a reporter with little risk professionally or legally.

While I understand I represent the minority on this topic -- the best data I've seen shows the net effect of having guns in the house is to be LESS safe, not more. While it's a complex issue, I think cheering individual success stories (like this one) and dismissing the failures (accidents, etc) can lead to evaluate the costs vs. benefits incorrectly.