Hard to say what she was thinking when he asked for the ID. Typically, you pull out an ID and just what the problem is. Any other response....just gets you into hassle. Sounds like she was asking for trouble.
My understanding of Arizona law is that you are only required to show ID if you are stopped while driving. I don’t know what provision is made for giving a citation to a jaywalker who doesn’t show ID, because they have to be identified in some way.
I think both sides could have tried harder to keep this from escalating. However it is always better to comply with police requests and complain later if you feel there is a reason to do so.