It's not psychobabble. There is extensive evidence showing that stress and depression result in pain, that FMS is triggered by stress, and that psychosocial factors are important in recovery. The same is true for CFS and IBS, which overlap with FMS.

And the pain isn't muscular in nature, it is neurological.

I've done extensive research into this area for 15 years, written a book about it, and published research, as well as suffering from it myself (and recovering).

Although I haven't digged very deeply into Sarno's theories, I can tell you that from what you have posted above, it is right on the money. However it's not simple 'stress relief' or 'relaxing muscles'. It's more to do with rewiring your brain through changes in behaviour.