I work at a front desk for an ER. We dont even require a reason although we ask for on the paperwork and of course if someone thinks they are having a heart attack etc we would make sure the nurses got there right away. People can stick with illness or personal if they prefer. I cant believe she asked to see it and Im sorry that you went through that. Unless she was a nurse doing triage she had no right to do that and I highly doubt that because it would be done in private.
Sounds like a pretty bad experience
I hope you never have to deal with something like that again