وَإِنْ كَانَ مُسَافِرًا لَا يَسْتَضِرُّ بِالصَّوْمِ: فَصَوْمُهُ أَفْضَلُ، وَإِنْ أَفْطَرَ، وَقَضَى: جَازَ.
Translation: If he is a traveller for whom fasting causes no harm, fasting is better; nevertheless, it is permissible to omit the fast and make it up afterward.
The author explicitly qualifies the traveller as one who is not harmed by fasting. In that condition, fasting is preferable, but the traveller may use the travel concession and subsequently make up the missed day.
Preference and permission must not be conflated. “Better to fast” does not mean “not allowed to break the fast” in the situation described.