I've never been asked to prove or document my disability as way to avoid the Nude-O-Scope. I state "I cannot assume the position" for the MMW, and perhaps mention "rotator cuff injury." Since I recently got Global Entry and go through the PreCheck line, I've not had any issues anyway.

In the past, there have been a couple occasions where the TS"O" argued with me about whether or not the backscatter involved radiation, when I declined to be irradiated and requested a pat down. I ask if they are licensed to practice medicine (they never are), mention that I am so licensed, and offer my (not very sincere) sympathies that they have to stand next to the radiation machine all day long.

I do have a disability with the requisite placard, but my disability usually does not affect my ability to raise my arms.