Somewhat Injured Player?

[Freddy]

BV. Big schools.
Shooter fouled on drive. Hits floor. Stayed down for about four seconds as players rushed to him to make sure he's okay. He gets up, seems a little shaken but not limping or holding onto any particular part of his body like someone who wouldn't want to get his two free throws out of the deal.
He walks straight past the free throw line and toward his bench on other end. Coach, who never came out onto the floor, sends sub to table and horn blows. Sub is beckoned in by trail and he trots to the free throw line.
Seemed odd, yet transpired so seamlessly.
Caucused briefly with partners and said, "Can they do that?"
Top-of-the-head decision to go over to the coach and ask, "Coach, that player needs a sub because he's injured and can't shoot his free throws, right?" Coach says, "Yes."
I'm thinking: "Sure. Fine way to get a better free throw shooter into the game to replace the guy who can't hit the barn side of a broad." Except the somewhat injured guy was one of their hottest outside shooters with about 20 points in the first half already.
Still wondering about it.
I don't think that, by rule, we have to have the coach prove the guys is too injured to shoot his free throws, do we?
Anything I'm missing in the book that evidences the idea that we allowed something we shouldn't have?

And don't call me a plumber.