A: I'd guess that the reason your friend continues to play down his injuries is an understandable concern for his job. But by doing so, of course, he may actually be putting his job in jeopardy. The more his boss believes his recovery to be complete, the more critical he will become of your friend's performance. So I'm not sure that loyalty comes into it much; you just need to take every care not to do more harm than good.
The key issue is the likely speed of his full return to physical and emotional wellbeing - so it would help a lot if you found out what his medical prognosis is. You should be able to do this perfectly naturally when asking him how he feels he's doing.
If his advisers have every confidence that he'll be back to his old self reasonably soon, I think you could safely have a confidential word with his boss. Explain that your friend is putting a brave face on things but knows he's struggling. Given a little more patience and understanding, he'll achieve full recovery even more quickly. If your boss has any sense (and a bit of a heart) that should have an immediate effect and your friend need know nothing about it.