Is that a regulation? You are correct that a part/aircraft goes "back into service" when the flight starts as a revenue flight under the part for which it's conducted, the point though is the mechanic approves the aircraft for that return. That's the airworthiness release, the mechanic/CH saying the aircraft is airworthy. On any and all flights, the PIC accepts the aircraft and is responsible for it's airworthiness, which is what the sentence you quoted refers to. It seems like the semantics issue I brought up before.