So this is not legal advice and I'm not an immigration lawyer. And I'm not explaining how the law is likely to be applied. Instead, I'm explaining how an aggressive government prosecutor could plausibly seek to apply it.
The wording of 8 USC 1451(a) is not limited to particular questions on visa or green-card applications. The statute refers to how the "order and certificate of naturalization were ... procured" which arguably encompasses everything leading up to the order and certificate. Moreover, the statute has two separate prongs for revocation: (1) the "order and certificate of naturalization were illegally procured"; or (2) "were procured by concealment of a material fact or by willful misrepresentation."
The way government prosecutors interpret these statutes is to push each of these terms and prongs as far as they can logically go. For example, you could argue that the phrase "illegally procured" encompasses any unlawful activity that has some arguable nexus to the visa or naturalization process.
As to the second prong, 8 USC 1427(a) sets forth extensive requirements for who qualifies for naturalization. The requirements are extremely vague and broad:
> No person, except as otherwise provided in this subchapter, shall be naturalized unless such applicant, (1) immediately preceding the date of filing his application for naturalization has resided continuously, after being lawfully admitted for permanent residence, within the United States for at least five years and during the five years immediately preceding the date of filing his application has been physically present therein for periods totaling at least half of that time, and who has resided within the State or within the district of the Service in the United States in which the applicant filed the application for at least three months, (2) has resided continuously within the United States from the date of the application up to the time of admission to citizenship, and (3) during all the periods referred to in this subsection has been and still is a person of good moral character, attached to the principles of the Constitution of the United States, and well disposed to the good order and happiness of the United States.
That third requirement is so broad that almost any fact about a person could be deemed material to the naturalization decision. Now, remember that 8 USC 1451(a) only allows naturalization to be revoked based on concealing or misrepresenting material facts. So it must be the case that you were arguably required to disclose the fact to the government at some point and either didn't or misrepresented the fact. But if you made an omission or misstatement on any government form ever, that could be fair game for bringing revocation proceedings.
I am also not an immigration lawyer. In Maslenjak v. United States (https://www.supremecourt.gov/opinions/16pdf/16-309_h31i.pdf), eight justices disagreed with the expansive interpretation of the statute you describe. From the majority opinion, "The statute Congress passed, most naturally read, strips a person of citizenship not when she committed any illegal act during the naturalization process, but only when that act played some role in her naturalization." and "Suppose that an applicant for citizenship fills out the paperwork in a government office with a knife tucked away in her handbag. She has violated the law against possessing a weapon in a federal building, and she has done so in the course of procuring citizenship, but nobody would say she has “procure[d]” her citizenship “contrary to law.” That is because the violation of law and the acquisition of citizenship in that example are merely coincidental: The one has no causal relation to the other."
So that case involves 28 USC 1425, which doesn’t have an expressly-stated materiality requirement. The holding of the case is that, nonetheless, the statute requires an omission or misrepresentation to be material, which the Court defines as information “that would have mattered to an immigration official.”
8 USC 1451(a) has an express materiality requirement, which I addressed in my comment. The standard of what “would have mattered to an immigration official” can be seen extremely broadly in view of 8 USC 1427(a). In the context of the false statements statute, 18 USC 1001, material facts are those that have the “tendency” to influence the decision maker, but need not actually influence the decision. United States v. Gaudin, 515 U.S. 506, 510 (1995).
The materiality requirement provides some protection. It’s doubtful revocation could be premised on someone having illegally parked their car when going into a USCIS interview. But the standard for materiality is still quite expansive and leaves a lot of room for aggressive prosecutors.
Iirc not legal advice but there are reasons why some people may not want to apply for citizenship, if something has happened since they got their green card and they'd prefer not to have to have to put on an application.
The wording of 8 USC 1451(a) is not limited to particular questions on visa or green-card applications. The statute refers to how the "order and certificate of naturalization were ... procured" which arguably encompasses everything leading up to the order and certificate. Moreover, the statute has two separate prongs for revocation: (1) the "order and certificate of naturalization were illegally procured"; or (2) "were procured by concealment of a material fact or by willful misrepresentation."
The way government prosecutors interpret these statutes is to push each of these terms and prongs as far as they can logically go. For example, you could argue that the phrase "illegally procured" encompasses any unlawful activity that has some arguable nexus to the visa or naturalization process.
As to the second prong, 8 USC 1427(a) sets forth extensive requirements for who qualifies for naturalization. The requirements are extremely vague and broad:
> No person, except as otherwise provided in this subchapter, shall be naturalized unless such applicant, (1) immediately preceding the date of filing his application for naturalization has resided continuously, after being lawfully admitted for permanent residence, within the United States for at least five years and during the five years immediately preceding the date of filing his application has been physically present therein for periods totaling at least half of that time, and who has resided within the State or within the district of the Service in the United States in which the applicant filed the application for at least three months, (2) has resided continuously within the United States from the date of the application up to the time of admission to citizenship, and (3) during all the periods referred to in this subsection has been and still is a person of good moral character, attached to the principles of the Constitution of the United States, and well disposed to the good order and happiness of the United States.
That third requirement is so broad that almost any fact about a person could be deemed material to the naturalization decision. Now, remember that 8 USC 1451(a) only allows naturalization to be revoked based on concealing or misrepresenting material facts. So it must be the case that you were arguably required to disclose the fact to the government at some point and either didn't or misrepresented the fact. But if you made an omission or misstatement on any government form ever, that could be fair game for bringing revocation proceedings.