Thanks for discussing this, as it really helps me to understand where you are coming from.
When I hear a person say "this country is sick" in the context of a recent crime, I imagine they're specifically referring to the perpetrators of crimes as being the ones who make the country "sick". I would not assume that it was the intention to group the victims with those who cause a country to "be sick".
Your other statements are of course all correct, but irrelevant in this context - we've already agreed that violent crime in SA is disproportionately high.
So to be clear: I don't think saying "this country is sick" equates to grouping everyone together as perpetrators, or writing off the country. To my mind, it is simply saying that our disproportionately high rate of violent crime indicates that South Africa has a major problem.