Even if you have a good reason to think that some particular connotation is the most probable, it's just one option among many. Here the rate of false positives will be high.

Sure, that's true. We might disagree about how high my confidence in a particular most-probable-interpretation of the motives behind a particular statement can legitimately be, but it's clear that for some statements that confidence will be fairly low.

I feel in such situations attacking one connotation over another seems like a dishonest way to dismiss a statement.

Do you have any sense of why you feel this way?

For example, do you believe it is a dishonest way to dismiss a statement? Or just that it seems that way? (Seems that way to whom?)