Sounds like incompetence on their end.

I only had a problem with one station, and the rest would do it seamlessly in like 5 minutes upon showing them the adress and the passport. That said I did not tell them it's an airbnb or something, and they did never asked.

Btw, In Shanghai, i stayed at a friend's house and so did the online registration (it was my first night after arriving) and it was approved on the spot. The police then came to friend's house like 3 days later when I was long gone and they then called me and asked where am I etc. Was not a problem, but its just intresting.