The only times a doctor has manipulated my penis was during an STI check.
I had some weird redness on the head of my penis a while back, so I went to a local STI open clinic. It turned out to just be caused by the harsh bodywash I was using at the time (stay away from AXE bodywash!)
After taking a brief history, the doctor (40-ish mustached man) asked me to "go ahead and slip down your pants"
I stood up and complied, holding my tshirt up and out of the way, exposing myself from about my knees to my nipples. He held my penis in his hand for a long time, looking at the various trouble spots.
When he was done, I pulled up my pants, and he actually called in a second, much younger doctor in the clinic into the room for a second opinion. I thought he was just going to describe the problem, but to my surprise, the second doctor asked me to "please lower those, if you wouldn't mind"
Now I had two entirely clothed doctors, one older and one younger looking closely at my penis while the younger doctor held it and moved it around in his hand.
Moral of the story: maybe use AXE bodywash if this scenario sounds appealing to you.
(but seriously don't...)