God damn it, I initially quoted the China line to poke fun of OP with no intent of turning this into a Taiwon Numbah Won thread :P But I would like to respectfully disagree with your viewpoint.

I personally believe people should have every right to take offense when their government is threatened. A government's role is to protect the rights of its citizens; whether it be economic rights such as social welfare and education, human rights such as safety and healthcare, or emotional rights such as freedom of religion and speech. For example, Taiwan (or the RoC as you mentioned) provides its citizens with global healthcare, K-9 education, basic human rights, etc, and might even be the first country to legalize gay marriage. There should be nothing wrong for a person to recognize its government and be thankful for these kinds of services if one deems the services to be fulfilling; patriotism is not innately bad. In the case of China (or the PRC) and Taiwan, we have seen time and time again the denials or delays of Taiwan's participation in global organizations. It can be something minor such as the twisted representation of "Chinese Taipei" in the Olympics or something much more dangerous like the denial of health information during the SARS epidemic.

The governments of Taiwan and China are fundamentally very different; thus, the existence of patriotic Taiwanese (or any nationalities) should be fairly natural. Should people be offended by OP's simple mistake? Hell no, that's actually dumb. Should people be offended when their rights and integrity are challenged (directly, indirectly, literally, and figuratively) ? I don't see anything wrong with it.