I assume that when you mention that Samuel Yount always told his family that Phoebe was their aunt you infer that Phoebe was a sister of Samuel and that Enos Yount was the father of both. I believe that may be possible if Phoebe was born in the early 1830s. The 1830 and 1840 Census records for Enos Yount in Shelby Co., Ky list a female less than 5 yrs in 1830 and 5 to 10 years old in 1840 that I can't account for. There are two females 5 to 10 years old in the 1840 Census one of which is Lucinda Yount b. 1833 and 7 years old at that time. It is possible that the other female 5 to 10 years old is Phoebe Yount b. 1830 to 1831.
Phoebe Frances Yount married John Brown in Anderson Co., KY on Sept 30, 1858 acccording to Family Search LDS records. The 1860 Census for Dansville, Hendricks Co., Indiana lists a John Brown age 22 b. 1838 in KY and a Phebe Brown age 29 b. 1831 in KY which I believe is this couple and indicates Phoebe was born around 1831. The next Census record for this couple is the 1880 Census for Windsor, Henry Co., Missouri which lists John Brown age 45 b. 1835 in KY and Febbie Brown age 43 b. 1837 in KY and their children Thomas Brown age 14 b. 1866 in Indiana and John A. Brown age 9 b. 1871 in MO. Phoebe died before 1890 but the widower John Brown is listed in the 1910 and 1920 Cenuses for Clinton, Henry Co., MO.
I have been unable to confirm the birth date of Phoebe Frances Yount so the above assumptions could be incorrect. The Missouri Death Certificate for John Brown b.1837 unfortunatley does not include the name of his wife but the Death Certificates of his his sons do name their mother. Thomas J. Brown lists his mother as Mary Frances Yount and John A. W. Brown lists his mother as Frances Yount. It appears that Phoebe was better known by her second name Frances. At any rate the death certificates do confirm that I am researching the right John Brown/ Phoebe Frances Yount family.
I would appreciate confirmation of Phoebe Yount's birthdate and also the marriage date of Enos Yount.