It is these sorts of escape from logic that baffle me at times.
It wasn't her "word" that demonstrates the door wasn't closed properly at this particular time. It is the fact she could and did go through the door that demonstrates the door wasn't closed properly at this particular time.
Another glaring problem is from the dead body’s position, she never, in her best cop voice, ordered the “intruder” to stand up and put his hands in the air.
That's a lot of information to glean from the position of the body. I think any "conclusions" about this are mostly speculative.
She also didn’t do CPR or anything but let him bleed out.
You put a hole in someone's heart. They are dead. CPR will do nothing except pump the blood out of the heart faster. They call it "exsanguination."
Had the man been on an operating table with the finest heart specialists in the world, he was still likely a goner. You don't just fix a bullet in someone's heart.
You are right that she should have expressed concern and went through the motions of trying to help him, but there really was nothing she or anyone else could do for him at that point.
He was still alive, barely, when the other officers showed up.
What needed to be done for him was holes in important circulatory parts needed to be closed up, and this simply could not have been done before his blood seeped out of them. Of course they didn't know it, and the least people can do is to try to save him, but he was gone when she pulled the trigger.
He was still alive when the police arrived. A weak pulse but ALIVE. They did CPR. She didn’t lift a finger to help her supposed unintended victim.