I disagree, especially about the nurses. The medical system is a huge machine. Nurses and doctors are but cogs in that machine. The system produces guidelines such as "after looking at tens of studies, for patients above X years old, procedure X doesn't make sense"; it's way more important for doctors to be able to assess symptoms and to have a feeling for how to tweak those guidelines (yes, this guy is over 60, but he ran a marathon last week without problems, has never smoked, and his parents, both in their nineties, do not need care yet) than to know the ins and outs of statistics.
After all, all those statistics are kind of meaningless. They rarely are split by sex, age, smoking behaviour, and familial history ("Where was the study of nonsmoking 36-year-old neurosurgeons?") It's a doctor's job to, somehow, find the best approach using incomplete data.
More importantly, all guidelines likely are about approaches that have changed since the data was collected. That new anesthetic procedure may have shifted things by a percent, that slightly adjusted monitoring protocol another, the improved CT scanner another, etc.
Medicine just isn't that much of an exact science as many of us think it is. In many cases, we haven't managed to make it a science (yet). For example, in IVF, even after years of working together to copy each other's best practices, one hospital might have a 30% success rate, another a 40% one, even after normalizing for every difference in patient population or treatment we can think of.