Probably one of my best experiences in this regard came when I joined the military, at age 21.
I was a skinny guy, at that time, so I probably would have washed out anyway.
I was examined privately by an older man, the sort with the wild white hair 'mad scientist' look. I was told to undress to my shorts for the exam by the nurse and I thought it would end there. The recruitment information said that "female applicants, there will be no internal exam". And that even though I am male, I assumed that meant they would not be looking 'down there' for me as well. Thus, falsely reassured, we began.
At one point he distracted me with some innocent questions (can't recall exactly), and as my attention was away, he slipped on some white powderless exam gloves. The only hint i had that he was about to 'check downstairs' was when he then slipped his fingers into my waistband (as i was lying on the table), and tried to pull my grey briefs down. The band slipped from his grip and smacked me in the waist, and that was what got my attention.
Then he said "lift up". Raising my buttocks off the table to allow him to draw my briefs down to a little past my knees. The act of raising caused my penis to flop back towards my belly, better exposing my scrotum. He then checked my right testicle, rolled it around, gently squeezed, then told me to put my heels together and raise my legs. This tightens the scrotum and can make checking for lumps easier. He then did the same test to my right testicle again, then followed by a double dose on the left one. When he was done that part, he stopped for a minute to enter some notes, and then (with no warning at all) reached down to pick up my penis. In one quick motion, he rolled the skin back to look underneath, with the uncouth "Schlong working all right?". As he rubbed open the meatus to look at the opening, I was looking down at him and I said "no complaints so far". He the rolled my skin back up and told me to pull up my shorts.
As I was walking down the street later, recalling the incident of 15 minutes ago, I had a most raging hard on, which i hope the general public did not notice...(it was arrest worthy).
In the end, I was denied acceptance, because my 'heart rate was too high'. Well sir, that was because i was terrified of being erect in front of a (more or less) total stranger.
Probably better this way. I have not attempted to join again, because even if my heart was beating too fast, they may just sign me up anyway, and that is a commitment that i cannot make.