No, not every game. The first 2 games I was not sick. The first 2 however work did take me away a lot in day ones but I was still around. The 3rd game I had a migraine...and I was innocent in that game 2 by the way.
In fact if you want to look at statistics for a second...
game one: Grinch
game two: Govenor
game three: rolled as the Policeperson but was given innocent townie because Ice wanted someone less obvious.
game four: this one
what is the chance I've have a power roll randomly assigned to me 4 out of 4 times or even the chance of never getting an regular old innocent townie randomly rolled?