It appears that he has been thoroughly confused with his grandfather, Sir Robert Harcourt, and possibly other relatives as well.
Birth date is I think a typo (should be 1472?), and there seems to be some discussion over whether he had four daughters, or four *sisters* - either way, the family estates went to collateral male-line relatives.
Whichever "Robert Harcourt" was standard-bearer to Henry VII at Bosworth, it wasn't this one. Possibly it was second cousin Robert Harcourt (d. 1513), his grandfather's younger brother's son. In any case the heirs lost no time ingratiating themselves with the Tudors - Sir Simon Harcourt (d. 1547) entertained Henry VIII at Stanton Harcourt in 1534.
Descent of the manor of Stanton Harcourt from Domesday to 1988 can be found here: http://www.british-history.ac.uk/vch/oxon/vol12/pp274-281.