I believe controllers who have already been trained are allowed to have waivers as well, but to be accepted into the program you have to be able to pass the medical with no waivers. For example, having high blood pressure or being on meds for high blood pressure will DQ you initially, but if you develop high blood pressure that can be corrected with meds, you will not lose your job.
I got one for my hearing.Not true... many new hires are hired with a special issuance medical (waiver) for certain types of medication or health conditions.