I have not seen his Magna Charta Ancestry but I have seen postings Richardson made on this subject at Soc. Gen Medieval. If this is based on Shaw's History and Antiquities of Staffordshire (1798-1801), Volume I, which he cited at that time, and is the same reference cited in Ancestral Roots, Eighth Edition. AR8 Line 56A-35, "Proof that Joanna (Joan) was dau. of Rhys ap Griffith is given in Shaw's Hist. & Antiquities of Staffordshire I: 122, 126 and app. p. 38..."
Here is the problem, in Shaw's History, there are several mentions of this family not just on the pages cited and they don't agree on various details. The pedigree in the Appendix p. 38 is a correction to that on p. 404, and one of the differences is that on p. 404 it states "Joanna, called (probably with truth) heir of Stackpole, living 1402-3." That statement is modified on p. 38 of the Appendix: "Joanna, relict in 1202-3, had a remainder in her father's eftates on failure of iffue of her brothers Thomas and John", making no mention of Stackpole (the letter 'f' is frequently used for an 's' in publications of this era). But on both pages, it states that her supposed father “Refe ap Griffyth” was of age in 1328 ("a knight and teft."). That would mean that he was born at least by 1307, if not earlier, making him aged 64 in 1370 (date of birth given for Joanna in AR8 Line 56A-35). There are numerous other discrepancies as well, notably (with regards to AR8's account) that the widow of Rhys ap Griffith, Margaret, daughter of Nicholas Zouche, in an indenture dated 2 Henry V (1414/15) with her current husband William "Walfall" (Walsall not Marshall) on the one part and Thomas Griffith "fon and heir of Refe ap 'Griffith" on the other agree with regards to the inheritance of two manors. The indenture goes on with remainders... eventually, to "Lady Joan Vernon, "fifter of the aforesaid Thomas". So is she the daughter of Rhys ap Griffith? Look again at the dates. Rhys ap Griffith died in 1380, this indenture is dated 35 years later. To believe she is a member of this family we're asked to accept more chronological improbabilities. Consider also that this family occurs during the time of the Black Death in England. Even without the plague the average life expectancy for women during this time was age 29 and men 28 [Mellinger, Fourteenth-Century England, Medical Ethics, and the Plague, Virtual Mentor: AMA Journal of Ethics, vol. 8, no. 4 256-60]. The plague first occurred in 1348, returned to England in 1361-2 and remained intermittently. Initially it killed about half the population then settled down to 20-30% death rate in subsequent outbreaks. This makes the chronology of this family, if it is one family, more improbable. As for Joanna being an heir of Stackpole, Shaw's History mentions this on pp. 126 and 404, but fails to explain exactly how. Several secondary sources show Joanna to be the daughter of Richard Stackpole. This would seem to be not so much a case of which is the correct information, but rather which scenario is the weaker. Until we have good evidence otherwise, it seems Richard Stackpole is what we're left with. Jay