This statute reads:
Whoever falsely and willfully represents himself to be a citizen of the United States shall be fined under this title or imprisoned not more than three years, or both.
There is no restriction on whom or for what purpose the misrepresentation is made. For example, the following situation might occur: an American is considering whether to buy a house, so they talk to their prospective neighbours to ascertain the character of the neighbourhood. One of them claims to have born in Kansas and lived in the US for their entire life. After the American moves in, they discover that their neighbour lied and was an alien all along. The alien is convicted under 18 USC §911.
The federal courts upheld a conviction under the predecessor of this statute in United States v. Achtner, 144 F.2d 49 (1944) and upheld the constitutionality of the same statute in United States v. Tandaric, 152 F.2d 3 (1945).
However, in the decades since WWII, the Supreme Court has greatly expanded the scope of First Amendment free speech protections, so one might wonder whether the conviction in the hypothetical situation described above would still be held constitutional.