Some potential problems:
The "authorization was given by the parents and guardian..." This is a legal term only as the bonifide parents would also be the bonifide guardians of the person.
The Death Certificate identification of the father's name would be provided by the person identified as the "Informant." I often find the Informant's information was wrong. Her Death Certificate:http://www.sos.mo.gov/images/archives/deathcerts/1954/1954_0...
The informant was her husband John. However, his knowledge of the name of his wife's husband may have been only memory, or having no actual knowledge...this is common. This has more credence especially when he had no knowledge of the mother's name. The DOB of 1889, also may have been only his knowledge or memory, not supported by US Census...however US Census records are often wrong. Her birth identified as in Dunkin County would also need to be researched. You are facing some historic records which may have been "changed" by even Alice herself.
Records I find show she died in 1954, John in 1964, (but records also show she was born in 1892). If John was the informant, the name of "Ike" would only be as good as he knew/remembered in 1954.
-The 1910 Census of Ash Hill, MO
John Hartline, age 35, born in IL to father born in IL, mother in Indiana, farmer
Alice, age 37, born in IL to both parents born in TN
Rasias? son, age 4
---While this has a John and Alice, it does not appear to be the correct family.
The WWI Draft registration shows Lack John Newman Hartline born March 9, 1889 in Bernie, MO, a farmer with wife and 3 children.
-The 1920 Census for Liberty, Stoddard Co, MO
J.N. head 31, born in MO to both parents born in MO
Alice, age 28 (1891/1892). born MO to both parents born MO.
The 1930 Census for Liberty, Stoddard Co, MO
John N. Hartline, age 43, born in MO to father born in IL, farmer, first married age 15
Alice M. age 40, born in MO to both parents born in MO
Jimmie E, 17, MO
Bertha M, 16, MO
Rubby (sic) E, 12
Fred(erick) 23, widower
--The 1940 Census of Liberty, Stoddard Co, Mo
John N (provided info to enumerator), age 53, born in MO
Alice M, 50, MO
Jimmie, 26, widower
Ruby, dau, 2, widow
Pasil(as written), 18
Fred A Hartline (provided info), 33
Jerry R, 3
Harold E, 4/12 (Census enumerated on April 6th, so "probably" Dec 1939.