It seems to me that there are a lot of examples where belief diverges from belief-in-belief and when that happens, one should say so. This may be because of near-far divergence, but that is additional detail and one should treat it as such. There certainly are near-far issues that do not involve belief-in-belief failures. Maybe the opposite situation is rare. If so, then it is reasonable to jump from belief-in-belief to near-far. But first one should establish this. Until then, when one has a belief-in-belief situation in hand, one should distinguish between the hypothesis that it is the result of near-far divergence and the hypothesis that it is not. And one should ask how these hypotheses differ.
It seems to me that there are a lot of examples where belief diverges from belief-in-belief and when that happens, one should say so. This may be because of near-far divergence, but that is additional detail and one should treat it as such. There certainly are near-far issues that do not involve belief-in-belief failures. Maybe the opposite situation is rare. If so, then it is reasonable to jump from belief-in-belief to near-far. But first one should establish this. Until then, when one has a belief-in-belief situation in hand, one should distinguish between the hypothesis that it is the result of near-far divergence and the hypothesis that it is not. And one should ask how these hypotheses differ.