In the 1920 Census, my husband's great-grandmother and 2-great-grandmother were enumerated with a birthplace Saxony. There is a note next to the birthplace which may be in a different hand that says Ger (presumably for Germany). I have a passenger list from 1882 which seems to read "Saxony" as well.
Previous (1900, 1910) and later (1930, 1940) census records show the birthplace of the family members as Germany. The lazy genealogists' answer for this difference in reporting might be, "oh, the family didn't want to say they were from Germany because of the war". I'm putting aside this interesting social question for the more practical one: if the birthplace was recorded as Saxony in the 1920 Census, what did that mean? Does it mean where Saxony was as of 1 January 1920? My ultimate goal is to gather more information about the possible locations for the family's origin in Germany.
The article Wikipedia: Saxony (disambiguation) shows the problem: the Kingdom of Saxony (1806–1918), and the Province of Saxony (1816–1945) are two different regions. The town that has passed down in the family tradition as the place of origin is in modern-day North Rhine-Westphalia, which is covered -- if Saxony = Old Saxony. (Not likely, for reasons noted in this answer.)
Edited to add: Before I wrote the question, I didn't know that the subject heading for places in Germany in the Catalog of the Family History Library are based on Meyers Orts. See FamilySearch Wiki article: German Historical Geography.
I'd like to find statistics or research about the birthplaces recorded for German-American citizens in 1920. A table that listed all the provinces or regions that were recorded in the census would make it easier to see how the provinces reported in 1920 matched up with Meyers Orts.
Update: Some new digital images have been posted online at FamilySearch, and I have used the index card from the Index to New England Naturalizations to locate the naturalization records for my husband's 2-great-grandfather. His birthplace is listed as Werdau (in the Free State of Saxony).
So the mystery remains about why the family story said his wife was "from" the other town (in North Rhine-Westphalia).