Injured player

[The whistle]

I attended a lower level DIII Men's College basketball game over the weekend. I saw something that I had a question about. I officiate HS level and I know the ruling for HS but, maybe, it's different for College. Situation. Player A drives to the basket and gets hammered. Basket goes in and the player is injured. Coach/Trainer are allowed on the floor to attend to the player. Official gives the Coach the option to leave the injured player in to attempt the free throw. Isn't the player required to leave the court and the Coach allowed to substitute any player from the bench to attempt the free throw?