That is a wild leap to make. Just mind boggling. Dogs are not people, and people are not dogs. If that were not the case, a lot of the behavior and culture around dogs would be alarming, at best.
My favorite “theory” about this is based on the fact that they shot a reaction cut of Obi-Wan looking suspicious, implying that Han thought they were a couple rubes that wouldn’t know what a parsec was. That would mean it wasn’t a mistake, and you don’t need to come up with the convoluted shit other people have to justify it.
If he’s been at it long enough to paint a wooden sign about it, I think the authorities are aware.