You said: “if there was no valid marriage, Obama was not born a U.S. citizen because that requires the parents to be lawfully married.”
First, if Obama was born in Hawaii, then parents marriage status doesn’t matter at all: he’s automatically a natural born citizen. However, if he was born outside U.S., then different rules apply depending on whether he was child of unwed mother or American mom married to alien spouse etc. HOWEVER, “A marriage that did not conform to the laws of the country or state in which it was performed may be a void marriage, but only after declared so by an
appropriate authority, usually a court in the jurisdiction
where the marriage occurred. Prior to such judicial
declaration, the marriage may be considered voidable.
A voidable marriage is considered valid for all purposes
unless and until annulled or voided by the court. Even
after a marriage is voided, there is every likelihood that
the children’s status will not be affected. Every state in
the United States, for example, considers children of a
void marriage to be legitimate (see 7 FAM 1133 Exhibit
1133.4-2, Part II). http://www.state.gov/documents/organization/86757.pdf (pdf p. 37)
Thus, IF Obama’s parents really were “married” (i.e., there’s some sort of marriage certificate or documentation to prove this) but someone now wanted to challenge its legitimacy on grounds that it was void given Sr’s already being married, this would NOT affect the legitimacy of the marriage in terms of which set of citizenship rules might apply to an out-of-country birth.
No, I don't think so, although it is speculation.
I don't think they do good legal work either. I speculate the explanation is that they too at some point came up with Sec. 1409 (the statute making children born out of wedlock out of the country citizens of the US Parent); and because of its placement and adoption date concluded Obama had a shot at citizenship there; and started to lay the groundwork for the argument that his parents were not married. (As set out above on the legal site and above here somewhere, Sec. 1409 has an effective date identical to the modifications to the Sec. 1401(g) amendments reducing the time period condition to citizenship; and thus Sec. 1409 is not applicable to Obama.)