In my research, I have found (at least recently) you can be fined for ignoring, or lying on a US census document. However, I was curious if there are any known issues of the time (1900-1920 specifically) of people who immigrated to the US, lying on US census forms about their naturalization? If so, what would their reasons be for doing so? Or if it was not possible to lie about this, what steps did the US government take to verify naturalization claims, if any?
If it matters, the reason I ask this is because I am researching my ancestry, and my great-grandfather listed himself as having been naturalized for the 1920's US census, but he did lie or unknowingly put his wrong age, and immigration year.
For census records, bear in mind that they were sloppily done at times, and an ignorant relative or neighbor may have given details.
That being said, I've found one case in my research where the preponderance of evidence seems to indicate an individual was claiming to be a native born US citizen when they were an immigrant. They also lied about their age to avoid military service.
Did your great-grandfather live long enough to show up in the 1930 census? What is the information given there? There may also be state census in odd years (such as 1915 or 1925) which may shed more light on the matter.