More specifically, proprioceptive awareness is not itself a perception of the body as an object; for if it were, it would require an ordering system, a spatial frame of reference, that was independent of the body. Generally speaking, the proprioceptive spatiality of the body is not framed by anything other than the body itself. In other words, proprioception is a non-perspectival awareness of the body. (137f)
Proprioceptive awareness does not organize the differential spatial order of the body around an origin… Proprioception operates within a non-relative, non-perspectival, intra-corporeal spatial framework that is different from both egocentric and allocentric frameworks. Neither proprioception nor kineasthesia offers a perceptual perspective on my body. If they did, they would require a second body, or perhaps a homunculus that would act as an index. Our pre-reflective, kinaesthetic-proprioceptive experience thus plays a role in the organization of perception, but in a way that does not require the body itself to be a perceptual object. (138)
If the body itself is doing the perceiving, then such prenoetic operations provide specific conditions that shape perceptual consciousness. The body and its natural environment work together to deliver an already formed meaning to consciousness. (139)
Both Henry and Gallagher claim that proprioception is not perception and that the body as perceiver is not an object. But where Henry argues for a dualistic ontology where the subject as absolute life is always separate from the entire realm of the world and objects, Gallagher's understanding doesn't require taking any stance at all on that kind of metaphysical issue. Instead, as implied by his taking clues from neuroscience, he's more or less just describing and interpreting what we could call facts.
Both positions seek to reduce, or explain, what Merleau-Ponty left ambiguous, in particular given that, in Phenomenology of Perception, Merleau-Ponty continued to use the language of Cartesian dualism - the whole business of the body being subject and object, e.g. There's a lot to be said for being more clear about this, but there's still ambiguity in experience.
So, proprioceptive awareness isn't perspectival, but it is through proprioceptive awareness that our perspectives become intelligible as perspectives. I don't see myself seeing (as Henry says), yet when I see, the point from which I see is tacitly present. Or, to use Merleau-Ponty's famous/notorious example of the hand-touching/hand-touched, I don't feel my touching, but when I touch something, the posture of my touching, since it makes all the difference in the experience of touch, comes into awareness. Gallagher's argument regarding the non-perspectival character of proprioception is airtight (and "non-relative" hints of what Henry called the "absolute" knowledge the body has of itself), and it leaves us with the implication that, ultimately, neither neuroscience nor phenomenology can tell us why we have experience and not just sense data. Again, Gallagher's attitude toward this seems to be that meaningful experience is just how it is for human beings.
A bit further on the ambiguity of perception and proprioception: if the body's proprioception is its way of structuring pre-given meaningful perception, then, I would argue, we may not be able to take a perspective on perspective-taking, but we can get a feel for it, sort of peripherally.