I'm not a doctor, but running can definitely work out your back. Long trail runs with lots of elevation gain leave me with a sore lower back, mostly because "leaning into" the hill keeps my lower back muscles working to maintain posture. I've only experienced this when pushing lots of mileage on big hills, though differences in posture may result in different sorts of runs triggering this. My running buddy has complained about this on much shorter runs.

It's entirely possible this is useless for preventing back pain, or may even be bad for my back, but I wanted to share.