I haven't seen the law but my guess is that there's more to it, like political blackmail. I'm surprised any business person doesn't support the right to do private business with whom they choose, religious or not.
From the law (Capitalization in the orginal, not added)...
"5. "Person" includes ANY INDIVIDUAL, ASSOCIATION, PARTNERSHIP, CORPORATION, CHURCH, RELIGIOUS ASSEMBLY OR INSTITUTION, ESTATE, TRUST, FOUNDATION OR OTHER LEGAL ENTITY"
<<SNIP>>
"F. FOR THE PURPOSES OF THIS SECTION, "STATE ACTION" MEANS ANY ACTION
BY THE GOVERNMENT OR THE IMPLEMENTATION OR APPLICATION OF ANY LAW, INCLUDING STATE AND LOCAL LAWS, ORDINANCES, RULES, REGULATIONS AND POLICIES, WHETHER STATUTORY OR OTHERWISE, AND WHETHER THE
IMPLEMENTATION OR APPLICATION IS MADE OR ATTEMPTED TO BE MADE BY THE GOVERNMENT OR NONGOVERNMENTAL PERSONS."
http://www.azleg.gov/legtext/51leg/2r/bills/sb1062p.pdf
Since a Hospital falls under the definition of person as a corporation (or legal entity), then even as a non-government "person" they would be prohibited by law from taking action against another "person" (in this case an ambulance company or it's employee) that refused service based on religious beliefs. In addition, the ambulance company (and it's employee) are protected from ciivil suits so if the injured/sick person sues - they would be required to pay the attorney's fees for the ambulance company defending their negligence.
Do I believe that will happen? Personally, no. But technically under the law it could.