No, sorry for the confusion. As an example...mental health crisis shouldn't require police as the first response. But fire/emt won't respond, so police become the default response.

Personally I don't think fire/emt SHOULD respond to mental health crisis. There is a risk of violence there that they are not trained or paid for. But neither should police, whose training is "eliminate the threat" be the first response.

Either way, EMTs would still respond to your grandma having a stroke because that is clearly within their primary job description.

No, they are saying that fire/emt don't want to respond to calls that shouldn't require police, thus armed responders is left as the only option.