Why do they ask that?!

disclosing a crime for which one has not been arrested

People often ask me what rationale immigration could have for this N-400 question: 

• Have you ever committed a crime for which you have not been arrested?

They point out that if you HAD commited a crime, it's unlikely that you would voluntarily disclose that fact on your application and invite a criminal investigation, right? 

Well, yes, if you HAD committed a crime, you'd probably lie and check "no" with the hope that nobody would ever find out about it. But the reason they ask is illustrated in a recent news account here: http://windsor.patch.com/groups/police-and-fire/p/federal-judge-strips-child-sex-offender-of-us-citizenship_29aac1c4

The article is about an immigrant who became a citizen, and subsequently was charged with (and pleaded guilty to) sexual assault of a minor. The crime occurred before the man became a citizen, and of course he lied on his application (and at his interview) about whether he had "committed a crime for which (he had) not been arrested." Here's what happened next:

After an investigation by ICE Homeland Security Investigations uncovered Gayle’s misrepresentations to immigration authorities, the U.S. Attorney’s Office initiated a denaturalization action against Gayle in October 2012.

On January 29, 2014, U.S. District Judge Vanessa L. Bryant ordered Gayle’s citizenship revoked on the ground that he lacked the good moral character necessary for citizenship, and that his application for naturalization concealed material facts and included willful misrepresentations.

“For foreign-born individuals, citizenship is a privilege, not a right,” stated U.S. Attorney Deirdre Daly. “Mr. Gayle corrupted the naturalization process by concealing his criminal past, a past that included the repeated sexual abuse of a minor. The revocation of his citizenship is entirely appropriate.”