I see veilsides point and in the long run it would probably even lower our policies but I think having a dashcam provided by the insurance company may be a bad idea. You can only imagine that they'd tie together the ideas of the dashcam and one of those little black box things that records your driving data.
Nobody buys a 350z and then has a black box insurance for obvious reasons. Even if that means taking the car to a track. Black box says no.
Anyway, after what Dan @ flux said, I got myself one and will give my ins company a call to see if they would lower my premium. If not, oh well!