It's actually a question for your state association. They either determine what is an authorized health care professional, or in some cases (such as ours), leave it up to each local school board (in other words, they passed the buck). We can have a game between schools from different counties where an ATC is an authorized health care professional for one team, but not for the other. It's dumb, but it's the way it is.
But the state also absolved all officials from making any determination of who is or who isn't. The official tells the coach a player is possibly injured. The responsibility for having him checked by an authorized health care professional lies completely with the coach. If the player returns, the official is to assume a proper health care professional cleared him. The official doesn't have to chase down the health care professional, that's the coach's job.