Sounding like the NFL "on further review" I belive that 'Old Titsworth" was John Titsworth the patriarch of Rossville and father to Capt Edwin Newton Titsworth. When I read the Meeks claim initially I wasn't too sure if they were one and the same but giving the context and further reading in the history of NW Arkansas I suspect it was father -son.
Jacob A Meek located to Carrol county in 1837 from Tennessee with father Jeremiah and brothers William and Joseph. John Meek(s) was a son to Jacob I believe. Even prior to the war he had a bit of a reputation being charged with rioting (with 4 others) and indicted by a grand jury in 1838 eventually being fined $20. There are a number of entries for the Meeks Blevins clan in Carrol, Crawford and Franklin county histories most related to land and tax issues. Both John Blevins and Jacob and John Meeks have land entries in the Fayettevill land office listings.
"John and Alexander Boyd removed from Crowleys Ridge and settled on Long Creek below Carrolton. There were then living in the vicinity of Carrolton ..."Shotgun" Jerry Meeks, "Blue" Jacob Meeks,"Black"'Squire Blevins, Richard Blevins, Sam Blevins and others of Cherokee and English descent, whose society was not appreciated by their neighbors, as susequent developements will show." Pg 335 History of Carrol County.