The Role of Anecdotal Information in a Modern Health Care System

Some argue only scientifically proven methods should be used for treating patients. FDA style double blind studies to prove efficacy before patients get the treatment. Therefore anecdotes such as a patient saying some weird unstudied thing that helped them should be discarded as useless information - unscientific.
But where do ideas for new treatment studies start?
Weird anecodotal stories.
For example I was reading some comment forum on a documentary about autism. The vaccine anecdotes came up - a few parents saying soon after vaccination there was a fever, then they noticed the symptoms of autism appearing. It's easy for a health professional to discount this as parents looking very hard for someone to sue to recover the horrible costs and burdens of caring for an autistic child deep into adulthood. Lets call that the law-suit hypothesis. One parent said her son was sick a few years later with a fever, and behaviour returned to near normal, briefly. Now that's a weird annecdote, and doesn't seem to be tied to the law suit hypothesis.
If I'm a university researcher looking for something to research, I might pick away at that annecdote, by forming hypotheses:
H0: lawsuit hypothesis
H1: parent imagining things
H2: real symptom mitigation but unrelated to fever
H3: real symptom mitigation and related to fever:
H3a) something about the metabolism of the brain being reset lower during a (ie vaccine induced) fever during a critical brain growth period, and another fever brings the brain metabolism back to normal
To test H3a I might run a properly controlled studied (double blind, placebo control group) where I give some medication that increases metabolism of internal organs including the brain -I think thyroid hormone will do that- and if that makes a difference then I'll do more studies to try and isolate brain metabolism

A treatment may or may not result. The point is the annecdotes are very useful starting points for investigation. That's how a lot of discoveries are made in many fields. An accidental weird data or annecdote, further investigation and bingo. And annecdotes can come from outside of the research community. Inbreeding of ideas within a scientific discipline can result in stagnation, and annecdotes from non-scientific sources are a great way to open up new investigations.

Annecdote -> hypotheses formation -> scientific research -> dead end / new insight / treatment

But if I'm a researcher, or a health practitioner, or a health insurer or health system developer is there a way to systematically gather and mine annecdotes, since they can be so valuable? I think that's the next step in the evolution of modern health care systems.