Since the TSA cannot force you to prove it - after all, they're not medical personnel to evaluate it and not willing to risk your injury - whether someone lies becomes irrelevant.
"i can't raise my arms over my head" doesn't contain the word "medically". could be religious reasons, or simply personal superstition.
If they decide to follow up to make an example of you, they can easily record a video of you until you raise your arms over your head somewhere later in the airport or on the flight. You won’t have a good time proving your case.