Passports were not required by American Citizens to travel to and from Europe in 1897. The were recomended but again not required in 1915. Passenger manifests were written in the counrty of departure, so the person just may have assumed that the children were Italian born. As far as census records go, the emnumerator did not always speak to the head of household, or the spouse so census information coming from a neighbor or language barrier could have contributed to them being listed as US born. Some italian immigrant lied to census takers out of fear of the government. Do you know where in the US they might have been born to locate birth records? Also do you have a copy of the Naturalization papers, as a spouse and any children would be listed on the paper at the time of naturalization.