If you go through someones wallet and write down all the details required to open a bank account in their name, you do not suddenly own all those details, and y

If you go through someones wallet and write down all the details required to open a bank account in their name, you do not suddenly own all those details, and you may not do with them whatever you wish as if you did. Opening a bank account using those details is identity theft, because they are not /your/ details. No one cares if you owned the paper you wrote them down on.