Repetitive rocking is almost a primal response when you're in pain or distressed, so to me it would seem natural if someone with Fibro did this to soothe themselves.

Yes and I sometimes gently move side to side in bed. It is like a self comforting event. I do it unintentionally. SaraH132 said it best, it rocking back and for comfort.

Perhaps it is an instictual way to soothe. Many people rock when weeping in sorrow. Or a way to connect with your inner self. A form of meditation?
It is soothing that is for sure.
I'll be gently rocking and swaying.

I do but it is more like a way to diffuse the pain from fibro. It’s like I clench my body and then rock back and forth to loosen up.

I tend to sway with music,but I think I picked it up when I was constantly having to calm a colicky child. Rocking is a calming method and I would not be surprised if many people do it. Cymbalta made me a zombie too.