Of course it was. Organizations don't let coordinators make lateral moves, just out of the goodness of their heart. It was like when Shanahan let Heimerdinger leave his Assistant head coach - offense position with the Broncos for a lateral/down move to OC at Tennessee. I know lot of people said, "they let him go because it was Heimerdinger's dream job" or some crap like that, but it was a "firing".
Dinger did a horrible job here, and as Shanahan's good friend, it was publicly a friendly 'parting of the ways'.