I think most discrepancies on the census are accidental — due to uninformed respondents, language barriers, and census-taker error. But there are definitely cases in which people didn't tell the truth, for a range of reasons. One of my ancestors, a naturalized American citizen who had immigrated from Italy, sometimes told government officials (and her own children) that she was born in Kansas or Missouri. Who knows why — a desire to seem more American, nervousness, a fear of condemnation during World War II? Maybe all of the above.
I've also seen a few cases around the turn of the previous century where separated/divorced people living apart would list themselves as widowed on the census.