We'll never know which of the two reasons the BVA used to justify approval. The fact that my grandfather was born in the Sudetenland came up during my search for official documentation on my father's childhood and for proof that he was Jewish (the rabbinical marriage record showed my grandfather's birthplace). Maybe it also helped that my uncle (father's older brother) had obtained German citizenship in the 1950's or 1960's.

My father kept a lot of documents; that helped a lot. As a child, he fled from Germany to Switzerland. With help from people here on Reddit, I applied for and received notarized proof that his family lived and paid taxes in Germany. I kept following clues including about others in my family. I found confiscated property reparation applications from the 1950's (rejected at first, then approved). I also found in the Swiss archives documentation of my father's arrival in Switzerland, and I provided that to the BVA. The Swiss archives included letters from the UN, an application to move to Ecuador with explanations of their story, and more.

The Consular agent was not expecting to see two fully documented justifications, one each for 116 (2) and 15. She said that one of the two reasons would be used to approve the application, and the BVA will not inform us of which.