We are no different from NTs in the amount of over-reading and misinterpreting of hints between the lines. The miscommunication among NTs is rampant too.
What NTs do have that we don't is Theory of Mind, which is a (subconsciously acquired and used) theory, i.e. a generalized assumption (for the sake of common ground) of how all normal people will feel in a certain situation. So even if ToM is very often wrong in a specific case, it doesn't matter, because what it assumes is the conventional assumption, so it is acceptable. As long as you misunderstand what everyone else could've misunderstood, you're fine in society.
Eg. it's customary to blow someone off by saying "I'm too busy". NTs, because they have ToM, automatically interpret it to mean "I don't want to be in touch with you". This is often an over-reading of hints, because some people are honestly too busy. However, if you over-read the "I'm too busy" and think it's a hint to no interest, you're fine. Because you applied ToM - the generalized, common, conventional, acceptable assumption. Among NTs, in this example, the one in the wrong is the one who said "I'm too busy" - because he used an expression that almost no NT will ever take literally. He is judged as having been "misleading".
If someone understood what I mean and can explain it more clearly, I'll be grateful. I'm sure I haven't explained myself clearly.
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There are two means of refuge from the miseries of life: music and cats - Albert Schweitzer