the exam can be seen as embarrassing because it includes hernia check, genitals inspection, palpation of testicles, and a visual inspection of the anus while bending over and spreading the cheeks
The athletes of the school were given more thorough physicals than the students who were not athletes.
I was an athlete and our physicals took place in the locker room. Each student was examined without privacy while the other students were there. The students could watch the other student's physical from a distance or not. We were all naked while we were waiting for our physicals.