فِي السَّفَرِ وَالْحَضَرِ
During a journey and in settled residence.
Safar denotes travelling, whereas hadar denotes remaining in one's place of residence. Their combination removes the mistaken restriction of wiping over the khuffs to travellers alone.
كَمَا جَاءَ فِي الْأَثَرِ
As reported in the transmitted precedents.
The permissibility is thus tied to reported religious precedent, not merely to an individual's personal preference.