I found this very interesting because I often have the exact inverse experience. I am a theist, but when I have a close call like that my first reaction usually is "I got lucky." It's when my conscious mind kicks in that I start thinking ""Lucky" doesn't have to mean just "lucky," and God has worked in more mysterious ways before." (Which, yes, is precisely what you'd predict a theist would say if you asked one.) And then I start feeling gratitude.

I know people here would say that this must mean I don't actually believe in God and only believe I do, but if you judge real beliefs by first reactions then shminux has a point.