Supposedly these are on microfilm in the library in Hawaii.
I don't doubt it (too much), but that still doesn't prove a place of birth when one isn't actually listed in the announcement.
In case you havent seen it yet...
The New Englander And Yale Law Review, Volume 3 (1845) states
The expression citizen of the United States occurs in the clauses prescribing qualifications for Representatives, for Senators, and for President. In the latter, the term natural born citizen is used and excludes all persons owing allegiance by birth to foreign states.
http://www.freerepublic.com/focus/bloggers/2500780/posts