It reminds me of one recent story, about a woman from Ontario getting sent into secondary while trying to cross the border.
Then she claimed to be a US citizen, despite not having any document, and in the end, ended up slapping the border agent (NOT A GOOD IDEA, PLEASE DO NOT SLAP A BORDER AGENT). She's still denied entry because they cannot verify her US citizenship.
https://www.cbc.ca/news/canada/hamilton/kitchener-woman-slapping-border-official-1.4816591
I'm wondering now, if a US citizen shows up at the US border, asking to be let into the country, but he/she did not carry anything to show it, does the CBP have obligation to at least check whether the person is US citizen?
I know that CBSA has to attempt to verify the status of a traveller, if they claim to be either PR or citizen, but not sure about CBP.