Well, how about the other information I pointed out? Illinois was a free state. Missouri ended slavery effective in January 1865. The 13th Amendment was ratified almost 12 months later, December 1865. All that is verifiable, documented fact. So how was it possible for Mrs. Grant to still own slaves in December 1865 when she didn't live anywhere that slave ownership was legal? If you can answer that one then it might lend more credence to Mrs. Grant's memoirs.
The memoirs speak of the slave running away in 1864, so it fits in the time frame.
I just went down to the basement and blew the dust off Julia Grant's memoirs.
"Eliza, Dan, Julia, and John belonged to me up to the time of President Lincoln's Emancipation Proclamation.* When I visited the General during the war, I nearly always had Julia with me as nurse."
*Since Missouri was exempt from the Emancipation Proclamation, Julia Grant's slaves probably remained her property until the ratification of the Thirteenth Amendment in 1865.
Personal Memoirs of Julia Dent Grant, edited by John Y. Simon, University of Illinois Press, p. 83 ff.p. 88 by John Y. Simon.