The issue here is whether, under federal law, a person has to produce identification when requested by a federal police officer. She was arrested when she refused to produce ID by an officer, not the security guard. The guard called the federal police, who then asked her for the ID, and she refused. I don't know what laws may govern in that situation. The issue is not trespass, for many of the reasons you stated. It is whether she violated federal law in refusing to produce ID when she said she had it but would not show it to a federal police officer, not the security guard.
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And unless there is a law requiring one to carry an ID at all, it's downright unenforceable.