I think it is hard to imagine that evolution did not result in some hard-wiring of our reactions to the sight of blood.
Blood=violence, LOOK OUT!
Blood=violence, LOOK OUT!
And the various idiocies in traditional cultures about how to deal with menstruating women show that freaking out about this has been pretty common through history.
Sometimes it's for attracting, such as red apples, fruit/berries, or flowers. By attracting other animals, it helps the signaler.
Sometimes it's to signal danger, as in red poisonous mushrooms, or animals that have red bodies and are toxic or don't taste good. ("don't eat me")
I guess what I'm saying is that red was a signal long before humans came on the scene, and I think we are still on the look out for it because of those same evolutionary clues.
False negatives are.
A spat of blood may not mean danger, but if it systematically put you on your guards, you are likely to get an advantages over individuals who are oblivious to it.
Not necessarily violence, as yorwba pointed out, but the presence of some disruption or injury in the body that's producing the blood.