Even the NYTimes, which is usually pretty good for an obit, wasn't sure.
...
Evidently they did not have access to the US Census records of 1920 from New York City, or didn't bother to look.
From the Fox book we have
Living in Washington Heights (upper Manhattan)
Father: Rudolph Sr.,
Mother: Rosa
Sisters: Rosie, Julie, and Jerry
From the 1920 Census, we have in New York City the following entries for a family (screen shots below):
Living on 183rd St. (house number unclear) which is at the north end of Washington Heights
Head/Father: Wandderon, Rudolp, renter, male, white, age 37 married, immigrated 1907?, attended school? no, can read? yes, can write? yes, birthplace Switzerland, tongue Ger., ... speaks English? yes, occupation, superintendent, business Apt House
Family member: Rose, wife, age 38, year immigrated 1907, ...
Family member: Rose, daughter, age 15, immigrated 1907, ...
Family member: Julia, daughter, age 13, immigrated 1907, ...
Family member: Rudolph Jr., son, age 7, born in New York
Family member: Bertha, daughter, age 1 8/12, native born (illegible)
From this I conclude:
This family listed in the 1920 US Census was Fats' family,
There was some confusion by the census taker over how to spell both Rudolp and Wandderon. Note that Junior's name was clearly spelled Rudolph. The taker also thought that "Swiss" was a language, but corrected it to Ger.
Mom's real name might have been Rose or Rosa.
Fats was the first of the children to be born in the US after the family immigrated in 1907.
Rosie may have been named Rose.
Julia was called Julie.
Sister Jerry was actually named Bertha and was the baby of the family. Her mother Rosa was about 36 when she was born.
Here are the screen shots of the hand-written census: