Have you considered that they changed their surname? If you have no evidence that their name in Iasi was Schwartz, and you have researched your direct ancestors and their extended family in the United States, then a name change is a very likely answer.
I am working on a project on my Skorochod family line. I've discovered that different members of the extended family took the surnames, Hoodof, Rudolph, Rosenthal, and Badion. Any descendant looking for a passenger list with the American name would hit a very hard brick wall.
Risa Daitzman Heywood