It's a responsibility to ensure that the troops under your command, if they're injured, no matter how, have the injury documented and tracked. The system isn't perfect. But even if the soldier is injured playing hockey in CFB Petawawa, nothing to do with duty, there's an obligation for the chain of command to ensure that it's been documented.
I don't think it is very difficult, especially in this day and age. It's a simple form. When a soldier is injured, whether or not he's in an operating environment, the company clerks and medics all have this form and it's filled out. In the worst case, it can be done on a scrap of paper. If it's witnessed and annotated by chain of command, at least it serves as some source of documentation.
I don't think it's perfect. Do they sometimes not get filled out? Yes, unfortunately. I've been guilty of it myself. Sometimes you don't think it's a big deal, you don't fill it out, and then four or five years later you wish you had.