I have never had a "chaperone" per say for an exam by either a male or female practitioner. When I was a child, my mother was present until I was about 10, and occasionally a nurse, student, or resident may be present. (In the case of the last two, I was always asked prior to the exam if I consented) In the Navy, of course, you didn't question. You just followed instructions.
When I did exams, I did not usually have a stand by when examining females, unless it was a specific exam of the breasts, genitalia, or a DRE, and there was a female Corpsman available. Again, my patients were all military, so it was no big deal to them, but we had a female doctor in one clinic I worked in who always said "Lawyers are Doctors." (She must have missed the part that said as an MO, she can't be sued by a military patient. Ironically, she ended up marring a JAG lawyer.) The chaperone was more for my protection than the patients. Female military/Naval personnel have no problem stripping down in front of a male Corpsman if necessary.
As noted, there is, and has always been, a double standard. If a female examines a male, no big deal. If it's the other way around, it is (or was) once virtually a requirement. However, I am begining to see a change, and stand-bys are being used less and less frequency, and, as I noted before, it is more for the practitioner's protection than the patients. There have been cases where doctors have abused their patients, and also cases where they have been falsely accused of doing so.