The following information was found by an OKEY researcher. Note the reference.
1780, 7 Apr - Levin Okey appointed administrator of the estate of Thomas Okey "by special permission of the Orphan's Court." Wit: Philips Kollock, Penelope Kollock. (Sussex Register of Wills, R6-4545) Note: no record of this found in the Sussex OC records
1780, May 3 - Deed - Elizabeth Oakey, widow of Thomas Oakey, late of Sussex County, deceased, from Hugh and William Stevenson, sons of John Stevenson. John Stevenson had originally sold to Thomas Oakey who died before deed was recorded, 106 acres for 27 pounds. Wit: Rhoad Shankland, Robert Mariner. (Sussex Deed Book M-12, p326)
So, YES, Leven's father was Thomas Okey. Many of the records for this part of Colonial America are confusing in that some say Delaware and some say Maryland for the same area. I have learned to discount oral stories until I see confirmation in the records. I have chased several erroneous "oral" accounts. Check out my OKEY web page at Family Treemaker.