I'd give the psychopath button question a similar answer that I would to the smoking lesion question: what's the mechanism that correlates being a psychopath with willingness to press the button?
If being a psychopath (or not being a psychopath) affects your answer because it affects your ability to reason, then based on your psychopath status, you may not even have the ability to reason correctly and choose an outcome. The problem is ill-defined, because it asks you to do something that you may be incapable, by stipulation, of doing.
If it affects your answer in another manner, then pressing the button because of the outcome of a reasoning process won't be correlated with psychopathy even though pressing the button in general is. (Unless the button uses your decision as a criterion of psychopathy, in which case we get into halting problem considerations.)
Also, note that in everyday language, "only a psychopath would press the button" strongly implies that it affects your decision because it affects your values about killing people, which is the second scenario. It's also inconsistent because the problem statement implies that both psychopaths and non-psychopaths would consider pressing the button and would reject pressing the button only after figuring out the logic, but if a non-psychopath would always refuse because of his values, this implication isn't correct.
(Edit: Edited this lots of times. Phrasing my objection correctly is actually quite hard.)