Look at the actual Constitution. It assigns numbers to the Sections, not the individual clauses, and the original third clause of Article II is superseded by the 12th amendment. The more discerning text reproductions note that fact. The majority of birthers I've seen cite the NBC requirement as originating in the 4th clause as well.
That's why Arkeny has the following footnote: “The Plaintiffs cite the “natural born Citizen” clause as Article II, Section 1, Clause 5 of the U.S. Constitution, but it is properly cited as Article II, Section 1, Clause 4. See also Ind. Code § 3-8-1-6.”
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From the house.gov site:
Article. II.So again, WTF does Clause 4 have to do with the NBC requirement? Are you suggesting this activist state court in Indiana has it right, and the U.S House of Representatives has it wrong?Section. 1.
Clause 1: The executive Power shall be vested in a President of the United States of America. He shall hold his Office during the Term of four Years, and, together with the Vice President, chosen for the same Term, be elected, as follows
Clause 2: Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector.
Clause 3: The Electors shall meet in their respective States, and vote by Ballot for two Persons, of whom one at least shall not be an Inhabitant of the same State with themselves. And they shall make a List of all the Persons voted for, and of the Number of Votes for each; which List they shall sign and certify, and transmit sealed to the Seat of the Government of the United States, directed to the President of the Senate. The President of the Senate shall, in the Presence of the Senate and House of Representatives, open all the Certificates, and the Votes shall then be counted. The Person having the greatest Number of Votes shall be the President, if such Number be a Majority of the whole Number of Electors appointed; and if there be more than one who have such Majority, and have an equal Number of Votes, then the House of Representatives shall immediately chuse by Ballot one of them for President; and if no Person have a Majority, then from the five highest on the List the said House shall in like Manner chuse the President. But in chusing the President, the Votes shall be taken by States, the Representation from each State having one Vote; A quorum for this Purpose shall consist of a Member or Members from two thirds of the States, and a Majority of all the States shall be necessary to a Choice. In every Case, after the Choice of the President, the Person having the greatest Number of Votes of the Electors shall be the Vice President. But if there should remain two or more who have equal Votes, the Senate shall chuse from them by Ballot the Vice President. (See Note 8)
Clause 4: The Congress may determine the Time of chusing the Electors, and the Day on which they shall give their Votes; which Day shall be the same throughout the United States.
Clause 5: No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
The U.S. Senate has the same, only they don't specifically number the clauses. The NBC clause is clearly the 5th one.
Even the Senate web site alludes to the fact that the NBC requirement (like the Naturalization Act of 1790, and like the nonbinding Senate Resolution 511) has always historically been about 2 citizen parents:
" This clause requires that in order to take the oath of office a president must be 35, a resident within the United States for 14 years, and a natural-born citizen. This last requirement raises the question of whether someone born to American parents outside of the United States would be eligible to hold the office. "
As I said, the actual Constitution does not have specifically numbered clauses. Some reproductions of the text insert clause numbers; some do not. The more discerning reproductions place the original Article 2, Section 1 paragraph considered to be clause 3 in italics or a different color while noting that is has been superseded by amendment. The Senate version to which you link does that.
So for the purposes of inserting clause numbers into the text, the original Article 2, Section 1 paragraph that would have been called Clause 5 is now technically Clause 4. It’s somewhat silly and a point of interest to legal geeks only, but there it is.