What do the adductor group of muscles (i.e., inner thigh) have to do with back pain? Quite a lot actually. In traditional anatomy terms we learn that the role of the adductors is to bring the leg toward the midline of the body and rotate it outward. However, during real life activities when the foot is in contact with the ground (i.e., walking, running, playing sports, etc.) the adductors function very differently.
The adductors (which originate on the pelvis and attach to the inside of the leg) lengthen like bungee cords to decelerate stress (i.e., gravity and ground reaction forces) to the pelvis and lower back as we move side to side and forwards and backwards (see image). When the foot is in contact with the ground and the pelvis/sacrum and lower back has to move from one side of the body to the other (such as what happens during a golf swing, when ice skating and also moving from side to side to hit groundstrokes in tennis) the adductors lengthen under tension to control movements of these parts of the body.
Additionally, when the leg travels behind the body (i.e., into extension) during movements like walking and running the adductors lengthen to slow down the leg/hip and pelvis (see image). However, if the adductors are unable to lengthen effectively during these movements due to myofascial restrictions and/or dysfunction then additional stress is experienced by the major joints and other connective tissues that the adductors influence (i.e., hip, sacroiliac joints and intervertebral discs of the lumbar spine). Over time, this can lead to pain of the entire lumbo-pelvic hip region.