[Used Can]

Fun enough, I thought the exact same thing. He'll probably say he's Hayate's twin brother or something.

Anyway, it was never said Hayate went there using his butler uniform by mistake. Although, the dialogue boxes did say these were exhausting days for Hayate, but all the same, he went there wearing his butler uniform on the first day. My guess is he's got very little time to actually change clothes, that he simply went there wearing his butler uniform. I also don't think he expected to meet Luca. In fact, in the author comment in the final page it says "Why is Luca here so early in the morning?".