Then again, I often find in China that workers/officials/whatever make up the rules on the spot, depending on what they know how to do, or what they consider too mafan. So maybe some will just 'feel' like you need a visa and others won't.

I get a similar thing in hotels where they can't be bothered to register my passport with the PSB, because they don't get many foreign visitors and so e.g. the computer to do it is not turned on. So they just don't do it.

I would guess you could get a hole in the wall to take cash most of the time, I just never see it done. One problem with cash in China is that the largest note has a pretty low value given how inflation is going and how costs are in tier one cities. Chinese people seem to think this is some kind of image management thing, where if they issue a larger denomination everyone will start freaking out about inflation. But I guess it's moot given how cash is losing favor anyway.