Arthur knows that there are a good number of oblivious people here, so he's playing it safe. He's 100% human so even those who can feel magic won't know that he's part of the 'community' right off the bat, and even if they figure it out he'd rather not tell everyone right away what he does. Hillingdon may be a non-entity for most people, but Arthur knows some people resent them for harbouring the kinds of people who do exactly what he does.

"Sounds like you know him about as well as I do, except I didn't know he had a dog until I showed up today. I'm probably one of the few people who aren't acquainted to him because of Lily."