I'm confused, why are there two threads by two seemly legit posters about two different restaurant with almost identical wording to complain about the lack of fapiao?
What's going it? Is there some kind of racket going, a shakedown?
While I agree in principal that a good business practice is to always follow local regulations, but when choosing between not going into business at all or fudging over minor things, it's a tossup.
The only reason I can see for asking for a fapiao from my perspective is when you want an reimbursement from your work, school, or whatever.
As being the case, reimbursement should only be given for legitimate reasons, such as a business meal in this case or a living allowance. As with local custom, most people in need of fapiao will always ask ahead of time whether that establishment can issue a fapiao or not, if not, they simply ask the next restaurant.
Refusing to pay on the pretext that they don't have a fapiao will unlikely work because even if the PSB are called they will likely not intervene citing that this is a tax and civil issue and inform you that you would need to contact the tax bureau. You can file a formal compliant but I doubt that they'll come to your rescue. If you however, insist on leaving with out paying, then you are in fact breaking the law in the eyes of the PSB in which case they will probably in the minimum try to convince you to pay and resolve the situation peacefully.
On a side note, from your writing it is probably safe to assume that you are an expat and not a local dressed as one. That being the case, try not to give "laowai"s a bad name and start going around acting like jerks and making a scene.
I've just realized that I might have walked into a minefield with this one but here's my two cents anyway.