X Visa, presumably no residence permit yet, traveling within china?

Hi there,

My girlfriend has spotty internet so I'm asking for her. She's here on a study abroad program with an X type (duration of stay 000). She presumably doesn't have a residence permit and says their program hasn't taken them to register one with the police station yet. We had some trouble staying officially in a hotel because of this.

Can anyone clarify this restriction? We want to know if she can fly within China with no issues to visit other cities or if that requires the permit as well.