Pole says that Richard in the pedigree appeared 19 Edw. III, a good fit with the Richard of 1343 in the Discovery document you cite.
At a minimum, the pedigree is incomplete. The SW Heritage Trust (formerly Dev. Rec. Off.) has a will dated 1520 for William Reigny, clerk, son and heir of John of Eggesford. I find him mentioned by Oliver, who gives the following presentations:
1259 John de Reigney
1267 William de Mony
1315 Richard Reigny
1341 ditto
1349 ditto
1354 ditto
1380 John Reigny
1429/20 Thomas Hoper, Chaplain, Thomas Fford of Chawleigh
1450 John Reigny gent
1456 ditto
1462 ditto
1477 ditto
1489 Ibota, relict of John
1514 William Reigny, clerk
1548 William Cornwall by grant of Charles Copleston and his wife Anne, cousin of William Reigny, clerk
taf