If you were an AZ non-resident and working in AZ you would need to apply for a Withholding Exemption Certificate. Only residents of a few states (California, Indiana, Oregon or Virginia) who are working in AZ can get that exemption from withholding. I'm sure that is where their confusion is.
This does not apply to non-residents who are not working in AZ. You are a non-resident and you are not working in AZ so there is no withholding requirement vice having a requirement because you work there and that you need to be exempted from. There is no withholding requirement. Your situation is indicated by the form A4 box 2.
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