Thanks for the feedback Majugi and Pfail. I think I've figured a way to justify it with the internal logic of the game. Rather than the player character walking about with their own camera or mobile phone streaming their MTV Cribs episode, they're using the internal security cameras. That then accounts for 1) Why you don't see the character, 2) There's the image issues and 3) The Player sees a variety of stats and the chat while streaming.
As far as "fairness" goes, my understanding of the fair use doctrine in the US is that a person can use another's work as long as it is changed a certain amount and is then considered a new piece. While I don't think I'll be changing anything that much I will not be making any money from this work and I will be correctly attributing the creators.