Earlier quoted context omitted.
It seems like the question is fundamentally that of whether a given system can perfectly model its own state, but in this context that entails an implicit assumption that the brain's model of body state is perfect, which it is anything but.
I guess I don't really think any system would be able to model it's own state 100% accurately. Basically any model implies a reduction in information. I don't see what this has to do with pain perception in the brain. I am sure you could find an example in the animal kingdom of a creature which has pain receptors in its brain if you look hard enough.
If 'events at point_a' gets consciously interpreted by participation of cells one of which, lets call it point_b, is singularly dedicated to sensing events at point_a, we have a mapping in a mathematical sense from point a to point b. We know all such point_bs form a strict subset of the body, a part of the central nervous system.
If this mapping is continuous in the mathematical sense and a contraction, then a fixed point has to exist (a location that does its own interpretation). But the fixed point seems biologically implausible, that leaves us with the alternative that there has to be dead-zones -- places where events can happen but cannot be interpreted. (Example blind spot in the eye)
The way to avoid dead-zone would be to break continuity, or contractive property of the mapping.
> I am sure you could find an example … of a creature which has pain receptors in the brain …
I think my point would be easier to state for this hypothetical creature. If interpretation of pain is done by a strict subset of its cells and there is a one to one mapping -- at least one location b that interprets pain occurring at location a exclusively (presumably that's how the creature knows the pain is at 'a'), can this creature be free of dead-zones if the mapping is continuous and contractive. Can any creature free of dead-zones exist under those conditions. You claimed 'why not'. I am saying that if the mapping is a continuous contraction then either there has to exist dead zones or there is at least one self interpreting location.
To give another example of this phenomenon, if you spread the map of your city somewhere in your city, there has to exist at least one point in the map that sits exactly above the point it is representing -- the fixed point. The way to avoid this would be to have 'tears' in the map, or to have points in your city that are not closer on the map than they are in the city (that would be an unusual map).