I see what you are talking about now.--Gene
Edited to add ... For the immigrant, Anderson mentions him in GM2 (3), 224 (AmericanAncestors, by subscription), sketch of Roger Harlackenden, whose second wife Elizabeth Bosville married (2) by 1640, Herbert Pelham.
For this claim, Anderson cites "TAG 18:139-45."
Anderson's source is Meredith B. Colket, Jr.'s 1940-1942 article, "The Pelhams of England and New England." Colket states it is not his objective to consider the medieval family history, but does list sources for it. Colket's series appears in at least ?six installments/?seven parts, on AmericanAncestors, by subscription, 16 (1939/1940):129-132, 201-205; 18 (1941):137-146, 211- 218; 19 (1942):197-202; 20 (1943):65-76.
I didn't review these in detail, bur each is subtitled, Part "I An Interesting Heraldic Pedigree." Part "VI The Royal Lineages" One might review especially those two parts to see if the source of the false lineage appears, or if those articles repeated the falsehoods.