She doesn't absolutely need to be in Tainan that night and with all the advice on this board, she has decided to spend a night in Taipei (not necessarily in Taoyuan) before heading down to Tainan at some point the next day. I think the HSR station not being in the city centre was the straw that broke the camel's back, even though I told her she could just take a taxi from Taoyuan Airport to the Taoyuan HSR station.

Thank you all for your help and advice.