These kinds of laws exists in most country, but if you cannot prove it, they are useless. So if a employer has a public access to your health record, what you prevent him from doing the above and tell you a random reason ?
There was a case in France were an Ikea director has access to private police record and was making hiring decision based on that. It's completely illegal but they did it for years before getting caught.
Makes a lot of sense as well, anything else would be weird. If this was not the case you could just get it when you have already been deemed sick, to get the faster private care instead of public health care.
Lots of information is available in Sweden that would make Americans squeemish to have public. The difference is that most people aren't interested in the sordid details of their neighbors.