That document says that Elizabeth Charlotte Susanna (Amos) Beckford's great grandmother was on the ship, not her husband. Also, that document was part of the centenary so it would have been submitted in 1920 which would belie Elizabeth's or her husband's birth dates being anywhere near 1800. If her great grandmother and her great grandmother's children traveled in 1820 her great granddaughter is very unlikely to have been born in 1800.
As Deb says the document seems to be suggesting that 1820 ancestor was the wife of one of the 1820 settlers, Richard Bowles. She was the mother of several children called Amos who travelled with her. It was her G granddaughter that married Beckford. (who was not an 1820 settler) She is listed here simply as Elizabeth Bowles and is travelling with her husband and several children called Amos, http://www.eggsa.org/1820-settlers/index.php/settler-returns/1942-menezes-party But her story is not straightforward , as it appears her first husband may not have been dead(as she thought) when she married Richard Bowles. I'll leave you to read it . . http://www.eggsa.org/1820-settlers/index.php/additional-information/b-surnames/1494-bowles-richard-extra-data But certainly something to research further I also had a look at the National Archives of SA search engine, and apart from an American sea captain named Beckford who was around before the 1820 settlers, there are no records of Beckfords until much later. My only experience of researching the settlers is from one family but I have found several catalogue entries for them. There are lots for Amos (though of course turns up as a Christian name. There are also listings for Bowles including Richard Bowles death notice in 1851 and what is presumably Elizabeth's in 1854
edited 2nd link to make it work