Back when I was working for MedCan, a private medical firm here in Toronto, I often booked people for medical appointments that were utterly unnecessary. The job, in fact, pretty much required that I spend my time trying to get everyone to be tested for everything as often as possible because the company made money from each test. Even then I was still regularly in the position of denying people tests that they desperately wanted. I remember once there was a man in his 30s who wanted a PSA (prostate specific antigen) test done and I continually told him that although the doctor could ask for it if it was necessary we would not be doing it standard for anyone under 40. There was a long and involved fight back and forth between this man and MedCan with him demanding the test and us telling him we could not ethically give it to him. I think that rich people demanding healthcare that isn't helping them is a real problem nearly everywhere regardless of whether or not you have universal health care. The PSA test isn't even particularly justifiable on the populace at large, let alone those who fall outside the normal parameters.
This article got me thinking about the matter again and really showed how bad private healthcare can be. The author talks about how in a hospital he worked at a woman came in with the complaint that her breast had fallen off and asked to have it reattached. Clearly the individual case is horrifying but far worse is the note that the hospital didn't particularly panic because this wasn't out of the ordinary. Poor women who get breast cancer have this (automastectomy) happen on a semi regular basis because the cancer goes years without treatment and the hospital was used to dealing with it. That is the reality of private medicine; the rich getting tests that stand to make their lives worse, treatment that doesn't help, and fancy sandwiches in waiting rooms while the poor die of treatable illnesses. Even in Canada we have the issue of administering tests and 'cures' that simply aren't justified even if the cost were zero but it gets much worse when you have patients who are desperate and uninformed and the system is run for profit.
Innumeracy is as much at the heart of this as anything. People don't understand statistics and so they want treatments and tests without understanding that once false positives and other certainty issues are factored in that many things we do in medicine aren't producing any statistically significant benefit. I don't have a lot of hope in that situation ever being resolved though because if we can't get people off of credit card and payday loan debt I can't see how the much more complicated issue of medical statistics is ever going to be understood by the average person.