The chart only covers people *born outside the US*. If Obama was born in Hawaii, the chart does not apply to him.
Besides the chart deals with *Acquired* U.S. Citizenship at Birth, not necessarily "Natural Born" citizenship.
No court has ruled if those are the same thing or not. Mostly because the difference between "citizen" and "natural born citizen" only applies to eligibility for the Office of President, and there has never been a ruling on the matter. Let's hope there is this time. Although if Obama was not born in Hawaii then their will be nothing to decide, as he would not be a citizen at all, unless later naturalized, let alone a natural born citizen.
Yes, the chart covers people born outside the US, however the Naturalization Act was the same for people born within the US. It was all covered under the same Act passed by Congress:
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The laws regulating acquisition of U.S. citizenship at birth are among the most complex of the immigration laws. Adding to the complexity, Congress has significantly amended these laws on a number of occasions, in 1934, 1940, 1952, 1978, 1986 and 1994.
Throughout much of the history of the acquisition laws, the following 4-step analysis was required in order to determine if one had become a U.S. citizen at birth:
Determine the applicable law
Since changes in the laws governing acquisition of citizenship were seldom retroactive, the applicable law is usually the one passed immediately prior to the child’s date of birth. For example, if the child was born in 1949, the 1940 law would apply.
Determine whether one or both of the child’s parents were citizens of the U.S. at the time of birth
If both of the child’s parents were U.S. citizens at the time of his birth, chances are good that the child acquired U.S. citizenship at birth.
*****However, if only one parent was a U.S. citizen, the analysis must be completed in its entirety.*****
*****If the child had only one citizen parent, determine whether the parent had sufficient residence or physical presence in the U.S. prior to the child’s birth to convey U.S. citizenship on the child******
(((Ann Dunham was not old enough to convey citizenship))))
Prior to the 1934 Act, only citizen fathers who had resided in the U.S. prior to the child’s birth could convey citizenship. The 1934 Act provided that a citizen father or mother could convey citizenship to a child born abroad if he or she had resided in the U.S. prior to the birth of the child. Since the 1940 Act, things have become more complicated. The citizen parent is required to reside, or be physically present, in the U.S. for a certain number of years, some of which must occur after the parent reaches a specified age. Significantly for Filipinos, the 1940 Act, for the first time, provided that the residence of the parent(s) could be in the U.S. “or its outlying possessions”. This was important since the Philippines was an outlying possession of the United States from 1899 until its independence on July 4, 1946.
Determine whether the child lost his U.S. citizenship through failure to meet the retention requirements of the law
The 1940 Act added a retention requirement to the law of acquisition. This meant that a child born abroad who acquired U.S. citizenship at birth was required to reside, or be physically present, in the United States for a certain number of years before attaining a specified age. Otherwise, the child would lose his U.S. citizenship. The retention requirement only applied where the child had only one citizen parent. The 1978 Act eliminated the retention requirement. However, the Act did not restore the citizenship rights of persons who had already lost their citizenship by a failure to meet the retention requirement. Court challenges to the retention requirement, both on constitutional and other grounds, have proven unsuccessful. However, administrative decisions have granted exceptions where the child failed to meet the retention requirement due to his ignorance of his claim to citizenship until well into adulthood. (The retention requirement was eliminated prospectively by the 1978 law, and retroactively by the 1994 law.)
http://shusterman.com/acquisit.html