You make a good point. Many people who suffer from chronic low back pain do become "disturbed" by the pain and loss of function. This is a natural response to pain when the pain doesn't go away.
Tests of psychologic function can be helpful. Sometimes low back pain is linked with clinical depression. The real medical diagnosis is depression. In these cases back pain may be just a symptom. Treating the psychologic problem will help the physical problem.
It isn't always easy to tell which came first: the depression and then the back pain or vice versa. It is helpful to find out if there is a psychologic link in order to treat more specifically and accurately.