This was one of my first thoughts--these are extremely, extremely low base-rate events with not much measurement power. People mess with the surveys, or simply fail to understand the questions, or make mistakes in responding. The combination of them makes extrapolating very difficult. This was an internet sample too, and biased in that regard (which the authors acknowledge). It was interesting to me to read, though.

I think the bigger question for me, aside from this, are the benefits and costs associated with any response.

Even if you redid this and found that the likely percent of noncitizen voters was nonzero, you'd have to balance the benefits of any enforcement strategy against its costs.

Given that respondents were also saying that photo id didn't stop them, you'd have to also determine the number of citizens who were unable to vote because of voter identification. To me, the cost of denying a citizen a vote is much greater, and also more certain, than the cost of allowing a noncitizen to vote.

Overall, I'm concerned that the typical "innnocent before proven guilty" logic is thrown out the window when it comes to immigration, citizenship, and voting rights. The government should have to prove to some reasonable level of certainty that I do not have the right to vote, not the converse.