As far as I'm concerned...
Firstly, I think the public's need to electronically access this information is hogwash. The fact that some fact about a person is "public information" doesn't necessarily mean that it has to be made available over the Internet. There were pilot certificates and medical certificates long before the Web existed. A prospective passenger who is interested in knowing whether an airman possesses a valid medical (or even a pilot certificate, for that matter) can simply ask to see the certificate before boarding the aircraft.
Entities who have to do these kinds of checks frequently -- FBOs who rent aircraft, insurers, etc. -- may have a justifiable need to be able to do it electronically, but that doesn't mean the information needs to be searchable to the entire world. Access could be limited to those with a genuine need. If the FAA were a private organization, the government would be coming down on them like gangbusters for making all this information publicly available.
Secondly, even if FAA wants to argue that the survival of Western civilization depends on public' electronic access to pilots' medical certificate information, that could be accomplished by publishing the certificate class and expiration date -- and nothing more. Whether the airman does or does not possess a valid medical satisfies any possible need to know as far as the general public is concerned.
I also have serious doubts whether the question of whether the airman has an SI should be any of an FBO's or insurer's business. Unless they can show actuarial evidence proving increased risk, then it seems discriminatory, and probably illegal, for private businesses to overrule the FAA with regard to a person's fitness to fly.
Personally, I think all the information is made publicly accessible solely for marketing purposes. That's the only purpose I can think of that wouldn't be better served by a more limited approach to dissemination.
-Rich