No it shouldn't! He wasn't injured in the line of duty, he was injured while working on his mother's roof.
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.