It means that the individual has opted out of some kind of completely awesome event or plan for a very responsible and justified reason.
repeat offenders of the Patsy Out come to be known as either a patsy or a blitz; an individual who is never around for life's awesome moments because their own responsible nature prevents them from taking risks that awesome people would... also they are made fun of when they are not around.
fun friend: "Hey John, are you going to go clubbing with us tonight?"
Patsy John: "nah I need to have brunch with the girlfriends parents tomorrow so I'm going to Patsy Out this time."
1st guy: "hey why didn't Harold come camping with us?"
2nd guy: "I think he Patsied Out, said that work called him in last minute or something..."
1st guy: "Man if Harold keeps that up, he'll end up catching the curse of the Blitz."