Those saying to just let her go and find her later don't really understand investigations. THey have her there now and are actively investigating. They would have to put a lot of manpower into figuring out her identity, finding her, and by then any stolen merchandise would be long gone. And if she has no interest in cooperating now, why would she cooperate later. She won't.
Policing and crime investigation isn't a criminal centered system where the suspect decides the course of action. You can't say, I don't wish to be investigated for this crime right now so I am leaving and perhaps later if you identify me and find me, I might talk to you then. Or not and I will have destroyed or moved the evidence.
The whole attitude to here that if she doesn't want to be investigated for a potential crime when she doesn't have to be is weird. That isn't how policing works. If you get pulled over for speeding, you can't say, oh sorry, I am just going to leave and drive home and maybe some other time you can come find me to talk about speeding and then take off, banging into people as you go. All the people insisting she did nothing wrong and her actions are completely fine - were do you live?
In America being expected to stop when you are being investigated and told not to leave and not hitting people when you decide to drive away is not accpetable behaviour. No one thinks that will end well.
Not sure where the people who insist that police should just let her do as she wishes and just leave her be live. Never seen policing like that anywhere.