Yes, indeed until a few years back the Taiwanese passport just said "Republic of China". Often caused confusion and these were in circulation until very recently.

Taiwan is a self-governing territory but has not declared independence from China. Therefore it has not sought or been recognised as a country (though a few countries still recognise "the Republic of China" government in Taipei). This causes a number of anomalies - eg some countries have refused to stamp "Republic of China" passports (Vietnam used to be one such example, though since visas are usually supplied on a separate piece of paper to Taiwanese they would just stamp this instead). Also Taiwanese have to get a special travel document to visit the mainland. Taiwanese have to obtain many visas outside of Taiwan, though usually travel agents provide this service.

I think Taiwan is a special case when it comes to visa/passport stamping, whether it's local documents or foreign documents. Also what the Taiwanese authorities do today is not necessarily what happens tomorrow.