I've been to two AME's who gave physical exams that would have pleased the Marquis de Sade. They were very thorough. While I'm not unwilling to subject myself to a physical exam for the purposes of health, I don't want anything more than the cursory exam typically offered by an FAA medical examiner.
An FAA medical exam is intended to see that you meed the basic medical requirements to qualify as an airman. It's not designed to determine what other health problems you may have. You're not paying for anything more than a medical doctor to determine that you conform to approved data; 14 CFR 67.
I've been grounded twice by medical examiners. The first was when I began flying at age 15. The doctor didn't like kids, and tried grounding me for several items (among which was my resistance to having my eyes touched with a probe). The FAA approved all of them on appeal, and I was granted a medical certificate with no restrictions. On another occasion, an AME refused to issue my certificate because he centrifuged the urine sample, put it under a microsocope, and determined I "might" have a bladder infection. I really don't need something minor affecting my career, that can be handled through a different physician.
When your aircraft is given an annual inspection, no repairs are made. Any repairs are separate from the inspection. The inspection is done to determine airworthiness, and this means quite strictly, that the aircraft conforms to approved data. Does the airplane meet the specific standards written for it? Yes? It passes. No? It does not. The FAA medical exam proceedure is no different. It's not an indepth study of your anatomy or soul; it's a check by a doctor trained to determine if you conform to the medical requirements set forth for the issuance of an airman medical certificate.
You certainly could ask the doctor to look for anything he can possibly find, things that might ground you or damage your career, while he's at it. Do you really want to do that?
Personally, I'm grateful when I'm passed through the office quickly, with a minimum of fuss. I'm not there to risk my career.