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To my mind, this question relates to the accuracy of intuitions and the problems that arises while relying on it.
In the original post, my take is that the "quiet strain in the back of your mind" refers to the observation that people whom's opinion you value in a chatroom are discarding your opinion which is based on a single "anec-data" ; which, for a rationalist in his right mind, taking a step back and on a good day, would automatically discard as the sole model through which reality ought to be interpreted.
While this answers your question, my broader take is that untrained intuition is just a mashup feeling of what feels right or wrong according to a situation, and feelings are not to be confounded with reality. Unless... in the rare occurrence that these feelings have been thoroughly trained to be right, and by that I mean conditioning of the mind through repetition to the point that, for example, a veteran mathematician would "feel" or "intuit" something is wrong with a mathematical proof with just a glance and without going through the details.
Yet there ought to be human limits about relying on such trained intuition and feeling, thus, by default, relying on them must be a last resort or a matter of physical survival - which is what intuition is better used for (to me) - rather than to be extrapolated as a proxy for rationality.