Chinese activist who mocked Xi Jinping flees to South Korea on jet ski, arrested
(www.indiatoday.in)
I lived there and experienced it firsthand. All residents of China must apply to travel within China. These days it's mostly automated and quick for convenience, but you will be monitored at various checkpoints in the system.
For the most obvious example, you must register with local police within 24 hours of arrival in your destination, a service hotels usually provide free. This means that you must present your travel documents to check in to all hotels. This applies to all people, not only foreign individuals. Moreover, all lodgings are not legally registered to host foreign guests. So there are many hotels that non-Chinese people cannot even stay in.
I hope this helps relieve your incredulity