" if there is no way for them to do the job as stated in the job description without fundamentally changing the nature of the job"

the thing is, there are often a lot more possibilities than people who don't have the disability realize. I remember reading a discussion of whether Deaf people can be EMTs -- the EMT who was asked at first thought, "no way" but asked a friend who told them about a Deaf EMT the friend worked with, who sensed vibration instead of sound when using a stethoscope. It turned out there's an organization for Deaf EMTs.

(Also it sounds like they threw you in the deep end with responsibility but no power. That sounds extremely annoying.)