I have a friend who is a surgeon and he loved them. They keep the "unsick" out of the doctor's offices and most can fix a variety of problems with simple solutions.
Just because a physician can't find a problem isn't to say the patient isn't sick. The physician can at least apply what IS known about a patient's symptoms and screen out most problems that could make a chiropractic visit tragic.
But, sadly, there are a large number of people with painful conditions with no detectable etiology. You are right, once classified as such, some get thrown to the chiropractors.