Puzzle: is Rosa Pepper really Rosa Herdman?

My puzzle of the week is I'm trying to verify the adult identity of Rosa Pepper, daughter of Clarence Hearne Pepper and Minerva W Richards. In my previous blog entry, I list the record for Rosa as a child, living with her parents in 1910. I also show that in 1930, Clarence and Minerva are living in the same building as boarders with a Roland and Rosa Herdman. Rosa is exactly the right age. That would normally be proof enough for me.

However, if you look closely, Rosa Herdman's 1930 census says she was born in Pennsylvania, and her parents were too. That doesn't fit. Normally I would chalk something like that up to an error. But the proposed parents are living in the same building! Further there is no evidence that Clarence and Minerva ever left the Delaware/Maryland area.

The LDS new.familysearch (NFS) records provide a full name and birthdate for the daughter of Clarence and Minerva: Rose Minerva Pepper, born 17 Jun 1897. The birthdate from NFS cites their source as an extraction record. But I can't interpret it.

Birth date: 17 June 1897
Place: Chester, Pennsylvania
Contributor FamilySearch Extraction Program
Source Source type: Other, Image number: 202, Record number: 32, Batch number: I00299-7, Location in source: v 1 p 209, Source template: INDEX05, Locality: Chester, Pennsylvania, United States, Language: English - Repaging, Contributor: EXTRACTION

The Social Security Index provides information on Rosa Herdman and she has the same birth date, 17 Jun 1897 (see below). Normally that would be great proof, but it doesn't really address the birth place in the Census.

Rosa HERDMAN
Birth Date: 17 Jun 1897
Death Date: Jul 1980
Social Security Number: 221-50-2726
State or Territory Where Number Was Issued: Delaware
Death Residence Localities
ZIP Code: 21801
Localities: Salisbury, Wicomico, Maryland
South Salisbury, Wicomico, Maryland

The 1900 census is no help. The family is living in Sussex (if they ever lived in Pennsylvania) and Rosa's birthplace (and her parents) is listed as Delaware. And the birth date is January, not June. This muddies the extraction record.

Census 1900 Delaware Sussex Baltimore Hundred
family 165
Clarence H Pepper, head, W, M, Jun 1867, 32, Md 7, Del, Del, Del
Minerva W Pepper, wife, W, F, Dec 1876, 23, Md 7, 3 children 1 living, Del, Del, Del
Rosa M Pepper, dau, W, F, Jan 1897, 3, sgl, Del, Del, Del
Elizabeth S Richard, Mother in law, W, F, Feb 1835, 65, 8 children 8 living, Del, Del, Del

Can someone help me solve this puzzle? I'm looking for another piece of evidence that shows Rosa Herdman is Rosa M Pepper. Here are the kinds of evidence that would be adequate proof.

1. A marriage record of Roland Herdman and Rosa M Pepper. It will be about 1917, because Rosa said she was 20 when she got married and we know she was born in 1897.

2. Some other record of Rose M Pepper being born in Pennsylvania, preferably with her parents there too. Maybe a 1900 census of the family, which I've been unable to find.

3. A birth record of Rose M Pepper or other record that shows her birth year and month (and preferably day and place) Look in Chester Pennsylvania.

4. Any other record that shows Clarence H and Minerva Pepper lived in Pennsylvania at the time of Rosa's birth.

5. A clear view of 1920 census for the state of birth of Rosa Herdman and parents' birth. I have a poor copy of the 1920 census, and that part of the page is obscured by a blemish, which looks like a ink stain or tape stain. If this census shows that Rosa Herdman was born in Delaware, then it really looks like the 1930 census was wacky for some reason.

6. An obituary that ties these families together.

Oh, for what it's worth, here is the SS Death Record for Rowland Herdman:

Rowland HERDMAN
Birth Date: 21 Apr 1892
Death Date: Oct 1970
Social Security Number: 222-22-4277
State or Territory Where Number Was Issued: Delaware
Death Residence Localities
ZIP Code: 19901
Localities: Dover, Kent, Delaware