I agree the firing was justified - The main reason is the missing video from the cruiser. The officer as much as admitted that he also was taping the event. Most of the worst conversation happened outside the car. Possibly the Sgt. thought if he got rid of the tape, he had a chance.
Most depts. require the tape to be turned in at the end of the shift. It allows for an independent review of an officer's conduct and treatment of citizens as well as recording evidence.
Officers don't have an option, not to turn in the tape. It would be like not properly recording evidence and keeping it instead of turning it in to the evidence room.
The Chief has a defendable position on the tape alone.
Also, good training methods today have taught officers how to take a smart-mouth and verbally judo him with soft responses. The smart-mouth can actually talk themselves into admitting an offense. The Sgt. strongarm tactics are old-school.