Did Nancy Mack Humphrey Have Cherokee Roots?

Thomas H. Brown, nee Humphrey, was the daughter of Thomas H. Humphrey (also an ancestor of my niece and nephew).  It was thought within the family that there was a Cherokee ancestress in the family, enough so to apply for papers.  The lineage:  (Nancy - thought to be Cherokee and married to John Mack; daughter Nancy Mack married Simeon Humphrey; Thomas H. Humphrey was their son and Thomas H. (Humphrey) Brown was his daughter).

The Eastern Cherokees Application of Thomas H. Brown at Fold3:

Rejected

Source

Pertinent Information:

English Name: Thomas H. Brown (nee Humphrey)
Residence and Post Office:  Lehigh
County: Coal
State: Oklahoma
Age 31; born in 1877
Place Born: Rocky Comfort, Arkansas
Spouse: A. Dwight Brown
To What Tribe Does He/She Belong:  None

Children living with her as of May 28, 1906:
Dwight Brown, 12 years, November 6, 1896
Inez Brown, 9 years, June 17, 1899
Harrold Brown, 6 years, October 31, 1902

Give names of father and mother, and your mother's name before marriage:  (no claim is made through my mother's side)
Father's English Name: Thomas H. Humphrey
Indian Name:  None

Where were they born?
Father:  In the State of Georgia in 1844
Mother: (left blank)

Source

Father: My father is still living; Post Office Whitesboro, Texas
Were they ever enrolled.....: He was not enrolled

Name all your brothers and sisters, giving ages and residences if possible:
Mrs. Mable Fry, Fruit Vail, Cal, born 1872; living
Mis M. L. Humphrey, Mineral Wells, Texas, born 1876; living
Mrs. Fay Price, Whitesboro, Texas, born 1882; living

State English and Indian Names of your grandparents on both your father's and mother's side, if possible:
Father's Side:
Simeon Humphrey (no claim through Simeon Humphrey)
Nancy Humphrey (nee Mack) - Born in Georgia in 1815
Where did they reside in 1851...: Resided in Georgia until 1855, and then removed to Arkansas
Give names of all their children, and residences, if possible:
John Humphrey, deceased
James Humphrey, deceased
Thos. H. Humphrey, Whitesboro, Tex, RFD #5
Frank M. Humphrey, Bokohoma, Okla
Mrs. Mattie Madden, Rockey Comfort, Ark
Mrs. Martha Moran, deceased

Source

Nancy (Mack) Humphrey (no Indian name) her mother's name---and whom it is claimed is a full-blood Cherokee--was Cragmire* who was raised by a white family in Walton County, Georgia.  *Also spelled Craigmire and Cregmire in the file

Source

The application was rejected, but I cannot reject the idea that Nancy (Mack) Humphrey's mother was a Native American Cherokee.