An "investigator" made this claim in 1921 according to the Kansas City Sun, but the Sun couldn't verify it.
That was a fun xkcd!
I was curious as well, so I did some digging. (Luckily, we've got the internet, so it takes us a lot less time than it would have taken them!)
Weirdly, I found two separate places where these figures and foods were listed. In the first case, they were said by the Reverend Francis Higginson, an early settler in the New World, in his 1630 book New-Englands Plantation, who recommended that all travelers to the New World bring
8 Bushels of meale, 2 Bushels of pease, 2 Bushels of Otemeale, 1 Gallon of Aquavitae, 1 Gallon of Oyle, 2 Gallons of Vinegar, 1 Firkin of Butter; also Cheese, Bacon, Sugar, Pepper, Cloves, Mace, Cinnamon, Nutmegs and Fruit.
This was, however, not required, just highly encouraged. He also recommended
meale for bread, malt for drinke, woolen and linnen cloath, and leather for shoes, and all manner of carpenters tools, and a great deale of iron and steele to make nails, and locks for houses, and furniture for ploughs and carts, and glasse for windows, and many other things which were better for you to think of there than to want them here... 1 Iron pot, 1 Kettel, 1 Frying pan, 1 Gridiron, 2 Skellets, 1 Spit, Wooden Platters, Dishes, Spoons and Trenchers.
(All of this cited in George Francis Dow, Every Day Life in the Massachusetts Bay Colony)
In the other case, they were published in 1830 in the History of Saco and Biddeford, by George Folsom, which describes the origins of various towns in Maine. The exact quote, which references not New England but Virginia, is
A similar estimate had been previously made by Capt Smith with reference to Virginia. "Victuals to last one man a year; 8 bushels of meal, £2: two bushels of peas, 6 shillings: two bushels of oatmeal, 9 shillings: one gallon of aqua vitae (brandy), 2s. 6d.: one gallon of oil, 3s, 6d,: two gallons of vinegar, 2s." Total £3 3s, equivalent to $14.
This same piece was reprinted in The New England Gazetteer by John Hayward in 1841.
Someone who is more of an expert on early American history than I am could hopefully weigh in on what the deal is with this second piece, as I can't find an earlier reference to these foods/numbers being used in reference to Virginia as opposed to New England. But it's interesting nonetheless.