That isn't right, once you authorise someone to come onto the pitch the player has to leave, unless they were injured by a challenge that led to a caution.If the player has received treatment, then he must leave the pitch. If he's only been assessed, as in just checking if there ok, then I let them stay on the pitch.
if the referee has authorised the doctors and/or stretcher bearers to enter the field of play, the player must leave on a stretcher or on foot.