I do not think that we should ever decide that a player is not injured. (Well, you can decide that a player isn't really injured, but keep it to yourself!) If a kid tells you he is injured, he is injured.
Good idea not to emphasize that #15 has two shots. after the timeout, just follow your normal mechanics. I see nothing wrong with verbalizing that #15 has two shots, without any emphasis.
Saying, "I'm not sure that #15 is really hurt, butI'll take your word for it coach" will do nothing to improve the situation or game. Ergo, don't do it.
I also would not threaten to send a tape to the state office.
Having said all this, with a kid appearing to have received a bump well out of his comfort zone, I've used some lines like, "That was a pretty athletic play you just did. You have two shots coming..." It usually works - they get up to their feet quickly.