I'm not sure how this intersects with the point of the paper, but part of the problem with the Renee Good case (or things like it) in my opinion is that the focus too often is on the actual events at a particular moment, and not what is surrounding it.
I can see some argument, for example, that goes something like "Jonathan Ross was afraid he was going to get hit by a car and misperceived her as trying to ram him when was trying to turn right, so he fired in self-defense." Then there's a subsequent argument about whether it was reasonable for him to think that she was going to ram him, etc.
However, what's missing from this is a broader discussion about whether or not an officer should be putting himself in that position near a car at all, when it might be anticipated that there might be misperceptions about what is happening. Whether the officer is competent enough to perceive the difference between someone turning their car versus trying to ram them (especially at that speed). Whether they should have let medical personnel help afterward.
When you frame a discussion about perceptions of facts at a particular moment, you kind of get into a frameset of thinking that everything was passively happening, and start overlooking how a particular moment came to be and whether or not the real problems are a set of things that happened minutes, days, or weeks beforehand, and what happened in the time period afterward. E.g., instead of asking "did Jonathan Ross murder Renee Good?" you can ask "were Jonathan Ross and his colleagues competent enough to avoid a situation where they might feel justified in shooting someone innocent?"
I guess I feel like this "cultural perception" question often sidesteps more important questions about whether or not what came to be could have been avoided. This gets more deeply into the underlying attitudes or assumptions driving the perceptions one way or another and lets them be addressed more directly.