Not allowing a player to return for medical reason

[retiredumpire]

Retired umpire (and other positions also) here.  I don't do games any longer due to bad knees, however, I still attend games and have a question.

I know the rules state the officials have complete authority over the game.  However, in a recent high school game, a kid was sent off by white hat for medical evaluation. After the evaluation by a medical professional, the kid was given the clearance to return.  The white hat would not let him back in the game.  What's the rule?

[BetweenTheLines]

He can be sent off again if the player is exhibiting symptoms consistent with a concussion. If the player returns and in the officials opinion he is still exhibiting symptoms consistent of a concussion he will be sent out again. We can't make a player sit for the whole game but can keep sending him off.

[retiredumpire]

What rule would that fall under?

[NVFOA_Ump]

What rule would that fall under?

I believe that it would have to be 3-5-10-b along with the guideline for management of concussion at the back of the rule book.  If not concussion related ie: blood of some other clearly visible problem, that is solely up to the judgment of the referee.