No, the “No Jews, No Jews” saying doesn’t have anything to do with the perceived negativity of the news item. It has to do with the fact that Jews were involved in some way (good or bad).

I’m pointing out is that maybe that’s because Jews are just more involved in pivotal developments than are non-Jews.

Making this about “bad news” implies that there’s systematic racism against Jews in the news industry, and I’m sorry but that seems a bit far fetched.