And don't look at one individual case, look at the cause why this keeps happening.
The police force is trained that there is a high possibility that there is a gun. So how are they going to go in there? With guns drawn of course.
That is the difference. The knowledge of you might getting shot is enough to be trigger happy about everything. Especially when your training says the same thing.
But then it's not enough changing the training of the police force, whilst civilians still wield guns. Disarmament needs to happen on multiple levels.
And another thing, yes there are cases where it is fairly simple to tell if you are in front of a disabled or mentally ill person then a nutcase high on crystal meth. And these are just cops, without any training in the medical field to tell the difference and they go in already on edge. No wonder bad things happen.