Do you believe in premonitions/gut instinct about certain events? I myself just experienced a premonition on Thursday/Friday and it came true, and I had another one - that my Dad would die somehow on May 2nd - and I'm extremely worried about it since the first one came true.
Now, I'm a very rational person and would perhaps would be the least likely to disregard coincidence for something "un-scientific" like believing in a premonition/dream, but lightning does strike people and it does seem possible (empirically, anyway) that people have flashes of brilliance that foreshadow to something significant in the future. God exists outside of science and, perhaps, sometimes he sends messages down to people.
Take, for instance, the situation where James Woods was in an airplane and saw four Arab guys acting a little strange - he got the impression that they were preparing to hijack his airplane. Nothing was done but two of the guys turned out to have participated in the 9/11 attacks - inevitably, they did indeed hijack a plane.
Now, I'm not going to call "bleeding Mary" a sign of anything to come, but sometimes people get honest chills during stuff. Even if the incident itself never comes to pass, being a little more prudent to ward against future danger usually doesn't harm.