The story you link to is the one that is verified by all kinds of sources.
The story they still see fit to refer to in Swedish Wikipedia as an alternate theory, without calling it disproven, in mentioned in their Note #1, an article from 1948:
Ormond Rambo jr, "The first pioneers: The Rambo Family", American Swedish Historical Museum: Yearbook 1948, utgiven av American Swedish Historical Foundation, s. 1 ff
I think it is completely bogus. There is a small village by name Rambo up in northern Sweden - on the map today, and probably also in 1948, but having looked in old parish records I suspect it wasn't even settled until the 1830s - the first time it appears in the book is in 1836, one crofter family. In 1848 the family living there are still "nybyggare" (new settlers).