I think they do. The trooper turned sharply to the right to overcome the counter-clockwise skid caused by the impact. But he overcompensated and caused the rear end to violent skid in a clockwise rotation.
Given the assumption that the trooper would have had extensive defensive driving instruction on overcoming a skid, I conclude that speed was very likely a factor.
I am starting to envision a wheelchair bound Corzine as a media prop, akin to the late Chris Reeves.