If that theory was correct, then the kidnapping would have had to be premeditated, since the dog was gone on Monday, and Lisa disappeared on Tuesday (early am).
The other neighbor seems to be saying that she SAW Jersey following the dog around (whatever THAT means - wouldn't that be seen as really ODD - if you saw a grown man stalking a little dog?) and then the dog was missing. It's not proof, for sure - but it's pretty darned suspicious. It was very likely stolen, and not just a wander-off, because it was found over a mile away later that day. A little dog with no history of running off would just not likely go that far, that fast. We don't know if the dog was a perpetual wanderer, but her owner was pretty adamant that the dog was stolen (not just lost) and that Jersey stole her.