I think that all this is just an “interpretation” of the relevant visa law, but it does not seem to be stated specifically in the law.
Assuming that you applied to get a student visa of the “resident visa” type, then I think that you have to meet various requirements (such as establishing your desire to study at the school, maintaining an excellent attendance record during a period of having short-term visa status, etc.) so I assume that a “resident visa” of that type is not quickly granted.
However, in any event, if your application was denied, we could file an appeal, etc. and go through the judicial process to make sure that your rights are being upheld TO THE LETTER OF THE LAW.
However, during this time, it appears that you are in an uncomfortable position, i.e. either you have to leave Taiwan and come back in on a short-term visa in the meantime, or you just stick around Taiwan on an overstay status (not recommended . . .) so (in my opinion) it is up to you to decide what your best option is.