Thanks for the question! I've tried to answer any stuff like this in the description on the post page.
As per the description writeup: propaganda cards are shuffled into the chosen deck upon setup, and each faction may draw them as if they are normal cards!
Also mentions in the description that yes you've nailed it, the bad press IS free cardboard for everyone... If you aren't able to clean it all up by the end of your turn! The idea is that you don't want others to even SEE the news of your shady dealings, so better get rid of it for points before others do!
Thanks for taking a look, would appreciate your feedback on these two issues eh! ❤️