I think like Jimmy Johnson in his post 74 that the parents in a recent past (60', 70's, may be still 80's) chose always the most easy way to have their sons examined for school or sport.
If they had to choose between a physical examination at a doctor's 'private office or in a medical clinic for which they might pay and a report at school in a gym or a nurse's office for a group examination by a school doctor without any cost for them, it is obvious that they amlost always sent their sons at the school examinations.
it seemed so much more easier, more efficient and besides it did not cost anything and as it concerned all the students, there was apparently no reason for a boy to complain, he was treated like his boy's class mates.
I assume that they did not know always with details the set up of the group physical examinations since generally the students (at least in high school) did not like to relate with much details their school physicals, so it could happen that the families, especially the mothers, did not know how it was managed without privacy
as regards the fathers, I assume that most of them had known the same kind of physical examinations either at school or for the pre-military examinations, so they certainly did not mind a lot about the embarrassment of their sons, I assume that sometimes they found it rather funny and a good experience to make a male student get out of his false modesty if he had one.
The set up of the physical examination was decided mainly by the school authorities but certainly with the agreement of the school board, so the fathers who were members of the school board would have agreed with a set up without privacy.
At that time there was a wide spread idea about the useless of the sense of modesty for boys and male teenagers in an only male environment, they might grow up and become real man.
It is also certainly true that one reason for a set up of the physicals examinations in group without privacy was the will to keep the boys under control : more a male student was undressed, more he was normally obedient to instructions.
In the case of the Jimmy Johnson sports physical examinations at high school, it was obvious that there was no need to require that the student came at the physical wearing only a jockstrap, it would have been the same with a brief or a boxer, for the efficiency of the examination, so the school authorities wanted certainly to impress more the male students and why not to humiliate themt o keep them more under control
I understand that the male students were used to take showers in group and to change in the locker room in group but here it was different because they might expoose their naked butts to the sight of a large audience during a very long time and without understandable reasons.
May be in families the parents were thinking differently for their daughters : if they had the choice , I assume that they asked to their daughters what they preferred because there was sometimes a kind of double standard towards medical examinations, The parents were more concerned by the feelings of their daughters and cared about her privacy .
The worst for a boy student was certainly to be questioned by his parents about his physical examinations in front of a slighly older or younger sister who could tease him after his relation if he described it with details, for instance when he was instructed to line up with just jocks if his sisters knew what it was because they were never told to wear such underwears exposing all the butts