It used to be very standard practice. Eisenhower submitted his B.C.
http://www.sonorannews.com/archives/2010/100922/frontpage_Ike.html
Yeah. But Ike's B.C. was created in 1952. So it did not have the signatures of the attending physician, and/or witnesses. So it would not pass muster under the Arizona Bill.
All of the States doing this need to be very careful with their "or" provisions. By that I mean that there have to be provisions for Americans who weren't born at a hospital, with an attending physician. If States try to simply decree that everyone born at home, like Ike, or on the side of the road, five miles from the hospital, like a woman I know, cannot run for President, then the Courts will swiftly strike the laws down.
So long as a person in BO's place can still qualify for the ballot -- if his story is true -- the laws should be upheld. Absent judicial activism. And what are the chances of that? (/sarcasm)
If I had to predict right now, from most to least likely, I would say that (1) BO produces long form B.C., with some embarrassing info, and MSM media tears into Republicans for forcing the revelation. (2) BO claims that he had a long form B.C., but that it was destroyed, by court order, after one of his adoptions, then sues. (3) BO just sues.