That would make sense if he had underachieved, though. He won the Pac 12 twice in the last 3 years, and Washington isn't a place that is going to turn the screws on you hard if you go 7-5 after a nice run like that. I honestly don't know if there are any insane pressure cooker, fishbowl jobs in the Pac 12. Before you say USC is one, remember they just decided to keep Clay Helton around another year.
From some of the things I've read it feels more like self inflicted pressure by Peterson
In the Pac 12 there are places where football is more important than others, like USC, Oregon, Washington, etc., but I don't think there's any place in that conference where the admin/boosters/fans are as hellbent on winning as much as a place like Alabama, Oklahoma, Ohio St, etc.