Any statement that a company does not have to give you tax statements is utter and complete B.S.
The nice ladies in the Tax Office are happy to make a few phone calls to your boss to “explain” the tax laws. They did so for me on numerous occasions when I was living in Taiwan (like suggesting to the accountant that white-out wasn’t really appropriate for tax documents). In the case of no withholding statement being issued, it’s a little trickier, because while they will agree to call up the company in question, they will ask you to state how much income you had from that company and then you are liable for taxes on that amount. Now, just how vigorously they go after that company after they have the tax money from you is another question…you would have to follow up frequently and loudly, most likely.
The tax office seems to take a fairly lenient view on certain things, for example, my former employer who “forgot” to withhold taxes (after telling me on tape that he was withholding and forwarding taxes to the authorities monthly) with the result that I arrived at the Tax Office with a withholding statement that stated I had had zero tax withheld. To my knowledge, they never went after him (more’s the pity, they could have found all sorts of fascinating things.)
The 183 day rule should not have anything to do with being with the same employer AFAIK. However, it might have to do with being on an (any) ARC versus a tourist visa. Your “clock” might have started in May, and you may have inadvertently stayed out of the country long enough to not make 183 days…??
The only exception to not withholding might possibly be if you are working as a lecturer vs. an employee (category “gao3fei4” or one of the other weird categories instead of “wages”). But even then you are supposed to get a tax form from the person paying you money, even if it says zero taxes were withheld.
The nice ladies in the Tax Office in Taipei at least are indeed your friends. They’ll be glad to get on your employer’s butt for you. Just be careful about saying how much you made. In your cases, if they’re claiming you don’t have 183 days, you have a lot at stake as they will eat your 20% and you’ll never see it again, so it might be worthwhile checking it out.