How do you determine that “this is a specious distinction” is the conclusion rather than what follows in the sentence or the sentence after?

I think the easiest way is to recognize this as part of a pattern that recurs often in LR: some people claim X, but X is wrong, for reasons. In this pattern, "X is wrong" id the conclusion. More specific to the argument, we know it's the conclusion because the second half of the passage directly supports it.