What many don't know is that LEOs are told not to make any statement for 48-72 hours due to the amped state they are in immediately following a shooting.
There are two very important publications that folks should make themselves aware of that illustrate this quite well. The first is the DOJ's own Violent Encounters manual. The second is the January issue of US Concealed Carry magazine, with specific emphasis on the article named "Memory Distortions".
The memory distortion article illustrates two very real issues that can happen and exactly why you say absolutely nothing for at least 48 hours. One is the clear distortion of memories through time perception slowing, one example from the article was a LEO firing his pistol who couldn't figure out what the gold colored beer cans were that were flying past his head. They were .40 caliber pistol casings from his own pistol. Another is the complete fabrication of memories, known as false memories. False memories even impact witnesses, not just the shooter!
These, especially the last one, are also items that illustrate that NO eye witness testimony is truly reliable. Credible, maybe, but reliable it is not. I've even experienced the eye witness issue on a minor incident (non-firearm related) where 2 people standing side-by-side watched the same incident and dictated that they saw things completely different.
So let's illustrate something Ayoob isn't covering within those aspects. Someone attacked you. Depending on State law, that might not be enough. You may have to illustrate that your life was in danger or that you were facing serious physical injury per your State's statute.