I will claim ignorance in how LEOs work the legality of such, but in the military during ANY injury, whether on or off duty, an investigation (JAG) is conducted to determine if the injury was "In the line of duty" and has nothing to do with whether the person was at work or not. Lots of car accident injuries, home accidents, etc. are considered "In the line of duty" simply because there was no misconduct (illegal activity). If LEOs operate under the same presumption then the incident I cited would be precedent. If not, then all bets are off.
As a veteran of the US Army, I understand where you are coming from. As you are likely aware, as an enlisted soldier at least, you are available for duty 24/7 in many assignments, and the property of the US government. Your actions are basically at the whim of your commanding officer, often even in your off duty time, so such a policy has merit. It never crossed my mind that such might be the case for LEOs, I see them as no different than any other state or federal civilian employee, but you raise an interesting point.