In addition to getting the paper from her, I would have at least tried to get her to show me some ID. If she refused, I would have told her it is either that or I call the police.
No. Do not do that. You have no legal right to do that unfortnally. Even if she is some kind of scum piece of shit, she still has the right to be protected sadily. Which means people that only deliver papers can't force her, or really even attempt to get her ID.