Cars are most assuredly NOT looking for pedestrians or cyclists. In this situation, I'd guess that the person that almost hit you was looking at ONCOMING traffic only, and as soon as that was clear, they figured they were good to go.

I almost got run down last year in virtually the same situation as you have described. The four lane roads like this are the worst, since you are further from the oncoming traffic, not to mention that pedestrians tend to be somewhat rare. On a two or three lane road, when I'm waiting for the light, I'll try to get a good jump when the light turns green and be out of the "kill zone" before any of the left turners can take me out. Four lane roads are often divided, and may have turn lanes to cross as well. In situations like this, it can be impossible to beat the oncoming left turners.

A bright front strobe, pointed right at the oncoming traffic is about the best you can do to get their attention. Even then, assume they don't see you, and plan escape routes accordingly. It was after my incident that I started running a strobe in the daytime.