The crux of some recent research into pain can be summarized in a few points:
* Sometimes you'll hear patients talk about pain and look at their area of pain and find nothing in their bones/muscles/etc that would indicate they should experience pain, and sometimes you'll look at other patients and their bones/muscles/etc and find they should experience pain but they don't.
* If you have three cups of water–two of them warm, the middle one cold–and stick a finger in each cup, your finger that is in the middle, cold cup will actually feel a hot, burning sensation. Try it yourself. Pain can be misleading and not indicative of actual danger.
* Similarly, ever play a sport and not feel an injury until the next day? (I'm not talking about soreness.) This indicates that pain can be silenced, and that underlying physical damage doesn't immediately and directly cause a sensation of pain.
The mind-body connection in essence is this: your body is the territory, and your mind is the map. Your map of the territory can become out of sync with the way the territory actually is. The body is incredibly adaptable, if you teach your body to feel pain, it will, if you teach your body to move freely, it will. This doesn't mean, if you're feeling pain, go and do crazy things and hump the dragon so to speak. It does mean: approach the dragon. Lean into the pain. Allow yourself to feel pain. Recognize the pain and listen to it and learn more about where the flare-up line exists in your body. Constantly strive to elevate where the flare-up line is, mindfully and with good vibes. :)
Increasingly we're moving away from a past where physical pain is stigmatized.
With that in mind, I don't think it's anti-scientific to think there may be legitimacy to other mind-centered approaches to pain relief.
To expand on your point for others about mental exercises: if you experience pain, say, in your leg during a squat, if you mentally visualize doing a squat, and imagine doing it while not feeling pain, and practice doing that visualization, that will help you feel less pain when you actually get around to doing a squat.
Another way I've heard people treat phantom limb is by getting a tall standing mirror, so that their other limb in the mirror looks like their missing limb. And then they will move their limb and that will help treat the pain they feel in their phantom limb.