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a.Any contestant who exhibit signs, symptoms or behaviors consistent with a concussion (such as loss of consciousness, headache, dizziness, confusion or balance problems) shall be immediately removed from the match and shall not return to competition until cleared by an appropriate health-care professional. (See NFHS Suggested Guidelines for Management of Concussion in Sports, in Appendix B.)
The Article does not specify whom should remove a wrestler from the match, referee, coach, wrestler or health care professional. The referee has authority to remove a wrestler from a match, including for injury such as loss of consciousness, headache, dizziness, confusion or balance problems. In the example cited, both wrestlers " go down" which can be evidence of a balance problem with the rules do not define.
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(3) A second occurrence of injury to the head and neck involving cervical column and/or central nervous system in the same match shall require the wrestler to default the match
I think it is pretty clear the referee will retain the authority to call the default. The referee will be closest to and most observant to both the first and second incident. The coaches view may be obscured by the position of the referee or wrestlers and the HCP may well be treating another athlete. Surely you would not expect the wrestler to make that call. If the referee retains the authority to default the wrestler incurring a second incident of loss of consciousness, headache, dizziness, confusion or balance problems, that is fair indication (since it is not specifically directed in the rules) the referee can refer the wrestler to the HCP for a review based on what he has observed in the ring. The HCP has the authority to call for the 5 minute HCP review, but as the entity responsible for the safety of the wrestlers in the ring, there is no prohibition the referee can make the referral to the HCP and since the ref has the authority to start the 5 minute clock, inform the HCP he is doing so.