I wouldn’t expect the verification to work across state lines. I wouldn’t necessarily even expect it to work beyond that single machine. Having people registered in multiple locations is a tougher issue like you say, but it’s not the main suspect of widespread fraud. This would be trying to address fraud at the precinct level by corrupt local officials. If every vote has to be recorded by the machine and the machine would reject the same person trying to cast a second vote, then it makes it much tougher on them to create a large amount of fake votes than would just filling in a stack of blank ballots. The most they could create would be their number of machines multiplied by their number of people involved in their scheme.
Yes, I had not thought too much about the fake vote creation back when I wrote my papers. I naively assumed elections officials were honest and followed the law. I agree that a properly designed machine could do what you say. But there are still lots of other requirements for that same machine that complicate the design.