I'm going to say something controversial here, but please bear with me. Your statement sort of encompasses several parts of this problem.
Some doctors are miracle workers (see [1] below), but most doctors are glorified auto mechanics. I don't say that to downplay the amount of intelligence/skill required for the job, but if you think of most doctors as "saving lives", then you obviously haven't spent a lot of time around doctors/clinics/hospitals.
Most doctors rarely save lives, and often when they do it wasn't them that really did the critical life saving steps, they're just the interface the sick person is interacting with. Most doctors deal with a series of inputs (symptoms and circumstances) and output a solution (diagnosis and remedy), which requires very little critical thinking on their part. Sick kids with the flu. Idiots that took too many drugs that need fluids, benzos, cypro, or an ice bath. People at mid-life who made shitty decisions for most of their lives and now need Lipitor/Coumadin/a treadmill/a gravestone.
The truth is most doctors get paid a lot because people erroneously assign to them the ethos of miracle workers, when most of them aren't. In fact, they often can't even do anything for their patients (see above, such kids with the flu, old people who've made shitty decisions their whole lives). The cures really come from researchers and pharma companies that come up with drugs and treatments for these incredibly difficult problems. If doctors deserve their paychecks, it's because they keep alive the illusion society wants. The illusion that when something is wrong, the doc will fix them up good. And indeed that's basically what the article is about. Doctors demand respect and to be paid to keep up the illusion and to deal with the bullshit.
[1] Obvious and important exceptions to this are ER docs and trauma surgeons, who indeed save lives. There are also clinical doctors, who work tirelessly with armies of researchers to try to find new cures for cancers, autoimmune and genetic disorders (among many other things). There are surgeons who come up with new procedures to reduce the invasiveness and trauma of procedures. These are the people that deserve the lion's share of the praise that goes towards doctors, and they should get the lions share of the money as well (some certainly do).
In this whole rant, I'm not trying to lay blame on doctors for the whole mess, because problems come from all sides, as I've hinted. Patients have unrealistic expectations of what doctors can do, the health industry is trying to low-ball doctors (not always without reason) to maximize profits, and many doctors who thought they would be genuinely helping people are realizing in reality that fate is largely decided before they even meet their patient (as a criminal lawyer friend put it, "90% of my client's case is decided before I ever meet him, but he wants me to work miracles!").
This is specifically why I didn't continue into medicine like so many of my friends. If you really want to help people, you don't become a regular doctor. You become a thoracic surgeon, or you do basic research, or you work in pharma, or you start a biotech. That's how you cure people. But no one will praise you for it.