"There's also a maximum advantage an offensive player can have over a defender."
The doc level at the time of the injury does impact the initial injury (higher level means more of a chance it is only for the game).The actual length of an injury is not determined at the beginning (only the estimated length). Recovery/treatment happens every daily update (using your current staff/infrastructure of that day).
Outside scorer is defined by a formula with JS/JR/DR as variables. Inside scorer is JS & IS.