In France we stop to go to a pediatrician very soon, generally at 12 age, and aftter we go to a doctor of our choice ( in fact it is our mother who choses the doctor for us )
There are obviously some differences, for instance we are never given a gown, and a private doctor (except if it is a specialist) is never assisted by a nurse during the examination, but ramdomly there can be a medical student who can be present, it is not often.
If you are an adult patient, the doctor will ask to you if you agree with his or her presence but if you are a pre-teenager or even a teenager, I doubt that you are questioned if you are alone at the examination room ( some mothers come with their sons at least until 15 or 16 age, other ones stop to come when the son is aged 13) )
Now for a pre-teenager or a teenager, most of the doctors ask only to their young patients to strip until underwear and during the examination either they pull down the underwear to look at the genitals either they lift the waistband of the underwear to have a look below.Normally they do not ask to remove it except for specific reasons.
And at school examination, there is almost never a mother present, the parents are informed by a letter that their son will have a school physical examination which is generally mandatory but in fact if a student at high school do not come the day of the physical examination, he is never summoned an other day. It was different in a recent past.
At a recent past, it was each school year and even sometimes like for me at middle school two other quick checking physicals at the beginning of each school term performed by the school nurse only and it was really a mandatory physical. We were summoned an other time with an other class if we had missed the day of our class.
The permanent school nurse was always present with the doctor, mainly a woman, they shared the examination room, so that the doctor saw what the nurse did, and the nurse watched at the examinations performed by the doctor and took notes. We were used to that process. There could be also sometimes a female nursing student to observe the examination during a training course,she was here to learn how perform the examination of a boy student, even at high school. No way to complain about her presence, we were told to obey to instructions of the doctor by a Pe teacher who supervised us in the locker room where we all together were instructed to undress and to wait our turn.
It could be embarrassing between 15 and 18 age if we were naked even for the weigh-in in front of a young nursing student but we might comply to the rules.