I misunderstood. I thought you had 3 different locations in "old country".
Yes, an alien did not have to become naturalized citizen but if lived pass 1940 than an Alien Registration Form he had to file. I agree that you should verify with at least 3 documents an ancestor's place of birth.
Where is the arrival manifest of the 15 year old Otto? I can only view Ellis Island arrival manifests since I don't have a paid subscription to Ancestry.
I found arriving NY EI :
Dentsch, Otto Basji, Hungaria 15 1893 1908 He is listed Hebrew.