Assuming this is a hypothetical question, if you are adept with computers, know a little bit about private investigating, and can act, you can find out just about anything about anyone, (excepting people like the President, & other high ranking officials, CIA, NSA etc.) There are armies of people charged with securing private records of people who could be targets of terrorists, and nutjobs. Although rare, even people in witness relocation programs are sometimes found.
Moving to a foreign country gives you a much greater chance to "disappear" or "start over", so a transsexual person who picks up & leaves the U.S., and takes on a new name & identity in an out-of-the-way part of the world where technology is limited has a pretty good chance of never being outed.
Nowadays, people are WAY too lax in sharing personal info online. Blogging under your real name has to be the dumbest thing there is. How many sites use security challenge question like "what is your pet's name?" Then a person puts a picture of themselves with their dog on their MySpace page, leaves the photos open for anyone to view, you go take a look at the comments under the photo and find one from the person's friend that reads, "oh, you look so cute with scruffy."
Trying to go 100% stealth was hard before the internet existed. Today, it's impossible. The sort of records you are referring to in this question are quite difficult to obtain without a court order or some Academy Award winning acting. Doctors are well aware of the Doctor/Patient confidentiality laws, and they won't supply you with any information. Any monetary transaction done with a credit card leaves a paper trail, but that doesn't mean you have a right to look at that paper trail. Even cash is not 100% anonymous because of serial numbers, DNA testing, etc.
All this said, unless you have a legitimate legal reason and the proper court orders to obtain the information you've listed, you have no right whatsoever to look at it. I pity the person who ever tries to invade my private life in such a fashion.