Love your experience - very intriguing!
The only similar experience for me involved being taken to a nutritionist by my boxing coach in my 20s. This lacked the official-ness of authority of your experience (an element I really liked).
My boxing coach (who was very straight & identified as religious-but-liberal btw) wanted my body fat "measured" which he said is what this Nutritionist does. He chuckled when he said, "This guy is Bi and judging by past clients I've taken to him, he'll probably insist on evaluating you when you're in the nude, so be ready for that."
I just shrugged in reply. Uh ok. I was nervous right away, but told myself, "Oh whatever, it's fine, I'm sure this guy is professional and I'll just do as I'm told and not make any trouble."
Coach drove us over in his car from the private gym where he trained me in LA to this guy's office, after a workout session. I was fairly sweaty therefore but it was extremely windy that day, plus Coach's wheels were a convertible sports car - top down - so a lot of my body perspiration got an air-dry from the drive.
I liked the Nutritionist right away, he was very no-nonsense but sort of warm about his stern-ness. His office was very private. He had a bunch of contraptions that were all new to me, for measuring aspects of the human body. The measurement of my body fat seemed totally bogus to me - not reliable. But whatever. I did as I was told. I was bare from the waist up. My Boxing Coach watches it all from the side.
Then the guy announces, "I'm gonna need you to strip down now, if we want accurate data on your body."
Coach chimed in with, "I told him that would probably be necessary. I'm sure he's fine with that."
"You can put your clothes on the chair," said the Nutritionist. They were both just staring at me.
I stripped, even though I had a sudden block of cement in my stomach. I was in my workout clothes, sweat pants, t-shirt, etc. I don't like jocks so had on tight briefs and when I got down to those the guy said quietly & casually, "Strip the underwear as well." I was half-erect - undressing in front of people does that to me no matter what - and I complied.
The guy grinned & proceeded to do a couple more tests before he got out a tape measure and took measurements of my body head-to-toe. Well, I was fully erect by then, standing there getting body-measured. My hard dick was waving around in the air. Nobody remarked about it. "Let's measure your penis here," the guy said, smirking. "Why not."
Coach said nothing about it. I submitted to being fully measured. The measurements continued down my hips and legs and then on my feet, too. "Ok, very good, you can get dressed now."
Driving back to the gym where I trained, I said to my Coach, "I'm not so sure all those measurements and tests were really needed. You know?"
He grimaced. "Maybe not, the guy is always over-thorough, I think. But he's a pro, he knows what he's doing and what he needs for the Appraisal. He'll email over his Full Evaluation in a day or so along with recommendations for diet. You did good - you were very co-operative."
I was fine with it all - but honestly I never felt like there was a choice. I was paying my boxing coach a good amount monthly to train me; either I went along with his methods or I didn't. I wasn't prudish, after all, so none of the Nutritionist's "stuff" traumatized me.