To get to the other side

Although there are no definitive studies, some research suggests that pedestrians crossing streets are at greatest risk when obeying signals in crosswalks, and that careful jaywalking may be a safer way to cross the street.

I'm naturally a little suspicious, but Greater Greater Washington makes an interesting point:

Most research on traffic safety focuses on narrow questions posed by the highway agencies that fund it. Basic premises, like the idea that "jaywalking" is intrinsically unsafe, are rarely investigated...
One useful data set was collected for New York's Vision Zero program. That city, where residents routinely ignore signals when they cross streets, can be thought of as a natural experiment. The majority of pedestrian deaths, and a far larger majority of non-fatal crashes, occur while crossing the street legally in a crosswalk.

I doubt the data really addresses the relative death rates associated with jaywalking vs using a crosswalk. But still, it illustrates one of the hard realities of managing the interactions of cars and pedestrians (or bikes) - no matter who was in the right, the person who isn't in an armored, high-speed vehicle usually loses a confrontation.