This is a well-known issue. For a while, some ten years ago, it looked like the situation was loosening up, but in fact it seems to have gotten stricter. I suspect this is largely due to the introduction of an online registration system linked to the PSB, which apparently will only permit entry of Chinese ID card numbers for guests if the hotel can't accept foreigners.
On their websites, many of the hotel chains mark out the properties which accept only Chinese.
As with much in China, there seems to be a lot of local variation. Some places the PSB seems pretty open and most hotels can take foreigners, in others it can be surprisingly tight.