Massachusetts pedestrians are only guaranteed right of way in marked crosswalks that do not have a signal. When there is a signal the light denotes right of way.
It can definitely happen. I'm guessing it varies state by state, but I was hit by a car while out running. I was crossing at a green light, didn't press the button, and a car made a left turn at the same time and hit me. The police report said the driver was not at fault.
The idea is that the higher purpose of a $1 ticket is creating a paper trail of jaywalking behavior that could be useful in court.