Having said all of that, most hotels in most places that travelers will encounter will have no problems registering anyone to stay. It's occasionally when you end up in some back alley somewhere and find a little hotel where everything is in Chinese and no foreigners are never anywhere in the area where you might end up being refused, definitely the exception, not the rule.
I was refused at several hotels within the last year or two. Doesn't matter what something you read says, many hotels off the beaten path do not accept foreigners. Many of them only have an RFID scanner which can scan Chinese national identity cards as the only way to register a guest.
There may be a new system which they don't know about/don't know how to use/don't care to upgrade to or maybe the newer regulations though may exist haven't actually been implemented in many places. I travel in China a lot and my Chinese is decent so I tend to look for more off the beaten path hotels that don't have any english signage or anything and regularly get turned away from some, even in Kunming in the last year. I also have a Chinese driver's license so sometimes they'll let me check in with that if they can. Not sure about the law regarding it but just know this is a reality that still exists. There are definitely situations where you can get away with it in a place that just can't be bothered, but most travelers will never end up trying to check into one of those hotels anyway. It's not that there is a regulation against foreigners staying anywhere, it's that the hotel has to have the licensing which allows for anyone including foreigners to stay at their hotel which is a bit of work that some hotels don't care to do and they may get into trouble if they are caught having foreigners stay there without doing the proper paperwork. At least that's how it's been since I've been here.
I've been refused many times in many cities over many years. It is not correct that if a hotel can register a Chinese that they can register a foreigner. Many hotels off the beaten path are not registered to allow foreigners and will turn you away. Most hotels on the beaten path are registered to do so so maybe you haven't encountered it yet. The Wen Lin hotel on Wen Lin Jie just around the corner from Salvador's doesn't allow foreigners to stay there last time I checked.
After a recent remodel and menu update this place has had a significant upgrade from its original iteration. Service, food, atmosphere have all improved. Menu could still use a little more variety but I still really enjoyed the new dishes that I ordered.