I can think of two situations where increased accuracy is detrimental: 1.) In maintaining moderation; 2.) In maintaining respectful social relations.

increased accuracy is not rationality

Think about it this way: if you want increased accuracy, then rationality is the best way to increase accuracy. If you want to maintain social relations, then the rational choice is the choice that optimally maintains social relations.

I think LessWrong considers rationality as the art of finding the best way of achieving your goals, whatever they may be. Therefore if you think that being rational is not necessarily the best option in some cases, we are not talking about the same concept any longer, because when you attack rationality in this way, you are not attacking the same rationality that people on LessWrong refer to.

For example, it is silly for people to try to attempt to increase accuracy to the detriment of their social relationships. This is irrational if you want to maintain your social relationships, based on how LessWrong tends to use the word.

The points I make have been covered fairly well by many others who have replied in this thread. if you want to know more about what we may have been trying say, that sequence about words also covers it in detail, I personally found that particular sequence to be one of the best and most useful, and it is especially relevant to the discussion at hand.