Matilde's father was Charles Rector per her marriage record. It is not clear to me whether he was a biological father or an adoptive father.
Since she is age 1 when with him (see records below), and she is alone at age 11 (living without parents, in another family) it seems Charles would be her biological father.
I've now searched US Indian census rolls in all the states mentioned in the records below, looking for Charles Rector, for his wife Hester Ann Smith, and for Matilde herself. I have not found them. Another volunteer researcher might have better luck ormight have access to a better database.
I also have not found the missing newspaper article.
It does not seem to me that a newspaper article can prove parentage. Newspapers print mistakes all the time. Regardless, it would be nice to find that missing article!
This is probably Matilde's parents getting married:
MARRIAGE Name: Hester Ann Smith Gender: Female Birth Place: NC Birth Year: 1823 Spouse Name: Charles M Rector Spouse Birth Place: TN Spouse Birth Year: 1816 Marriage Year: 1841 Number Pages: 1
1860 US Census Madison, Mercer, Missouri C M Rector 44 born about 1816 Tennessee, race white H A Rector 37 born about 1823 North Carolina, race white J L Rector 17 born Indiana Jesse Rector 15 born Indiana S E Rector 13 born Indiana L C Rector 12 born Indiana Heneretta Rector 7 born Illinois G W Rector 3 born Missouri M C Rector 1 born Missouri - race white <-------
1870* (P. O. Goshen) Madison, Mercer, Missouri Andrew Vanderpool 25 farmer Ann Vanderpool 28 keeping house Matilda Rector 11 born in Missouri * does not show relationship
1880 posted earlier - Mathilde was working as a servant
02 April 1882 MARRIAGE Decatur County, Iowa Wm. C. Gibson, age 29 born about 1853 Father: Garret Gibson Mother: Elizabeth Akers marriage to Matilda C. Rector born about 1859 Father: Charles Rector <---------------here's her father [as transcribed on Family Search]
1900 Leon, Decatur, Iowa William C Gibson 44 born January 1856 Missouri Matilda C Gibson 40 born January 1860 Missouri May Gibson 17 Ida A Gibson 14 Bert M Gibson 11 Lulu B Gibson 7 Eva G Gibson 5 Willa Gibson 1
1910 US Census (also posted previously) High Point, Decatur, Iowa William C Gibson 54 Mitalda C Gibson 50 born about 1860 Missouri Bert M Gibson 21 Lulu Gibson 17 Eva G Gibson 15 Willa M Gibson 11
The records are pretty consistent that Matilda was born in Missouri.
In the transcription of the 1925 Iowa State Census below, an Ancestry.com user has suggested the alternate name "Matilda C Rector" for this record.
01 Jan 1925 Iowa State Census High Point, Decatur, Iowa Matilda C Gibson 65, born about 1860 Missouri; race, white Father: Charles Rector born North Carolina, married NC Mother: Ganey Smith born South Carolina SPOUSE William C Gibson 69, born about 1856 Missouri; race, white Father: Garrett Gibson born Indiana Mother: Elizabeth Acres born Indiana Roll: IA1925_1686 Line: 30