The best approach should always be to hold maximally accurate beliefs yourself, even if you choose to signal different ones as the situation demands.
No, that wouldn't necessarily be the case. We should expect a cost in effort and effectiveness to try to switch on the fly between the two types of truths. Lots of far truths have little direct predictive value, but lots of signaling value. Why bear the cost for a useless bit of predictive truth, particularly if it is worse than useless and hampers signaling?
That's part of the magic of magisteria - segregation of modes of truth by topic reduces that cost.
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I was not aware that the universe was broken. If so, can we get a replacement instead? ;-)
Britain is broken, but Cameron's on that case.
Cameron just made a homeopathy advocate Health Secretary. Maybe the problem was Britain not being broken enough...