True, the long form certificate is not required but according to the bill, the candidate must prove that he or she is a natural born citizen. The short form certificate, which Obama has, clearly proves he is a US citizen. However, the term natural born is not defined in the constitution. This gives the state the option of refusing to put him on the ballot because the certificate of live birth does not prove his parents are US citizens which means the state interprets natural born as requiring that both parents be citizens. The state Democratic Party would challenge that ruling which would throw it into court. All it would take is a lower court to side with the state and Republican advertising would claim the court has ruled that Obama is not qualified to be president.
The better option for Obama is to submit his birth certificate, which proves he is a US citizen, and let the state decide if he is qualified. If they do not qualify him, then the Obama campaign can claim the state, which is controlled by Republicans are keeping him off the ballot for purely politically reasons. That would be an easy sell since most people, 77% reject the birther theory.
http://www.azleg.gov/legtext/49leg/2r/adopted/h.1024-f1-burges.pdf
Ahh, but here's the rub, you said:
However, the term natural born is not defined in the constitution.
Since whatever powers not specifically granted to the federal government are assigned to the states, as per the Constitution, then the power to decide what constitutes a "Natural Born Citizen is in fact assigned to the States. Agreed?
...And since Obama was born in the State of Hawaii, not the State of Arizona, it is the responsibility and right of the State of Hawaii to make such a determination, just like it would fall on the State of Arizona to make such a determination concerning one of their own citizens.
The specific determination made by Hawaii was that Obama is in fact a natural born citizen and thus has the right to run for POTUS.
Since Hawaii has already made said determination, according to the Consitution, Arizona cannot reverse that decision. Only the US Congress can.
That is not an interpretation, that is specifically written into the document in Article 4, Section 1, which states:
Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.
In addition, it was surely even the intent of the founding fathers, who sure as hell didn't approve of one state interfering in the sovereign rights of another state.
Now, since any natural born citizen has the right to run for president, Arizona would be denying that right by contradicting the legal judgement of Hawaii on this matter, thus contradicting Article 4, Section 2 of the Consitution, which specifically states:
The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.
Therefore, if Arizona declares Obama to not be a Natural Born Citizen, and then takes away the right to run for president, a right granted to him by the State of Hawaii,
Arizona is breaking the law in 2 ways, not just one.