The extra year is not something that is part of this process. It is a byproduct of it. If you don't start enrollment until January 2019 (which will be the effect of being granted a medical exemption) you effectively become a grey shirt so your eligibility clock does not start ticking until 2019 instead of 2018. This is not a Cael thing, more so it is a Teasdale thing or any athlete that chooses to defer enrollment.
In regards to the "magic wand" comment, this option is available to any student from the university in regards to academic progress. I'm sure it was available to you as a student as well - if you were in a car accident midway through the semester and were unable to complete your coursework due to being in the hospital for an extended time for example, do you think your university would penalize you if you wanted to return when healthy? That is the first part of the process. The 2nd would be if you were an athlete and wanted an exemption from one of the academic progress requirements, which then would be in the NCAAs hands.
A grey shirt if he does not wrestle for the team this year but if he does wrestle then obviously he uses one of his 4 years.