Remember this?
Obama himself, (not Nancy Pelosi) in December 2007, in order to participate in the Presidential Preference Election, swore to the SOS of Arizona that he was a “natural born citizen.”
From the post you linked, he used slightly different language.
He says "i do solemnly swear he is a natural u.s. born citizen"It seems nitpicky to differentiate between "natural born citizen of the US" and "natural born US citizen," but it is probably error to assume the two are identical as a matter of law.
The second incantation can be argued as using "natural born" as an adjective against "US citizen." It inclines one to adopt the fairly popular (but IMO, fatally flawed) legal approach that everybody born on US soil, regardless of the national allegiance and citizenship of the parents (except diplomat's kids), is within the group the constitution calls "natural born citizen."