I should disclaim that I would certainly agree to the statement "A dollar means more to a poor person than it does to a rich person," but I still find your level of incredulity a little surprising and probably disingenuous. It should be completely clear that the disagreement here is not about questions of fact but about what the question means.
(Edit: Actually, that shouldn't be completely clear at all. However, it should be clear that all reasoned disagreement is of this form. The process for most respondents is quite likely to go "Hear the statement -> Interpret statement as 'redistribution good' -> disagree" without regards for propositional content. If you want to get ridiculous results from interpreting people's statements literally, you could probably find statements much harder to justify than this one.)
What does "means more" denote here? In many contexts it is standard to evaluate strength of preference on a scale of dollars; according to this view everyone values a dollar equally. And there is pragmatic justification for this habit: if I want to determine who should receive a good, dollars are probably the best measure of strength of preference. If I gave the good to someone for whom it "meant more" but who was willing to pay less, I could implement a Pareto improvement by giving the good to the person who was willing to pay more and then performing an appropriate monetary transfer.
If we take this view, a dollar doesn't mean more to a poor person: everything else just means less. Maybe you think this is unreasonable (it is certainly odd), but if you allow any fixed yardstick (I'm guessing that most respondents who disagreed with the statement would have used bundles of particular comforts and discomforts as their yardstick) for measuring strength of preference, then you get similar artifacts--for example, people who care less about stress or physical pain, people who are willing to work harder, etc.
Interpersonal comparisons are inherently problematic and I think it is misleading to describe this question as an "easy" "ontological statement."
The other questions may be different. For example, on the gun control question it seems very likely that respondents are trying to signal their belief that gun control is ineffective by agreeing to a statement whose precise propositional content they haven't considered (just like incorrect respondents on most questions on both the original and the new test).
Silas Barta made the same point above, apparently more persuasively.
I believe it is generally a useful heuristic that if someone asks you a question and it seems to be true by definition, you are misinterpreting their question.
For example, if I ask you "Why are humans mortal?", and your usual definition of "human" includes mortality then you should probably not use your usual definition in interpreting the question.
A article in the Atlantic, linked to by someone on the unofficial LW IRC channel caught my eye. Nothing all that new for LessWrong readers, but still it is good to see any mention of such biases in mainstream media.
I break here to comment that I don't see why we would expect this to be so given the reality of academia.