The strong evidence to support this came from the studies of split brain patients. These patients were suffering from acute seizures and to stop the seizure from spreading to the entire brain the best course was to split the two halves of the brain through brain surgery.
The surgery was successful as anticipated in reducing the brain seizures but had some side effects. These patients were subjected to many scientific studies to see the effect of the surgery on their brain functioning by pioneering neuroscientist Dr. Michael Gazzaniga. Here is a video where Dr. Gazzaniga is interviewing a split brain patient:
The video clearly shows that the patient despite appearing completely normal has lost some of his ability to relate and interpret external items. Also, it shows how the left side brain acts as a interpreter and creates a story even if the story does not support the facts.