When you have documents that conflict in this way, one has to be wrong. Assess which one is likely more accurate. The 1907 immigration record documents them on a ship. While there may be some extraordinary reason why this record is wrong, for your purposes, it's safe to say they were on the ship. The 1920 census is subject to all sorts of possible errors. The enumerator, the person giving the information to the enumerator. All censuses should be used as good clues, not hard and fast facts. They are tertiary sources, at best, for immigration and naturalization information. I've found many errors for that information in censuses. And - the 1910 census agrees with the 1907 date, further questioning the 1920 census. If the person you referred to was naturalized between 1907 and 1920, there should be a record of it. Maybe you've looked already. In the NE US, petitions and/or declarations of intent for naturalization in this period have the immigration information on them. This is the document that would likely answer your question, but remember to cast your net as wide as possible when you come across these conflicts. Good luck! (1903 to 1907 is four years, by the way).