It sounds possible but it's a pipe dream. Trying to execute your plan is next to impossible. Also, what you outline is , like you said, perfectly legal. It's not rigging.
Rigging a national election: No way. People bitch about how inefficient the voting system is but that's what gives the system its security. While it might be possible to rig a few areas (very unlikely though) it's impossible to rig the whole country since each state has its own voting rules and system. Coordinating an attack on all the systems is not possible. But it's important to note that we need to protect the system so it doesn't become easy to manipulate in the future.
We see voting manipulation in movies as part of the plot regularly. I suspect that's why people think it's possible. It seem so easy but keep in mind that it's fiction. Just like Superman being able to fly.
If you want to manipulate an election, the way to do it is by using mass media to misinform the masses . If you control the media you control the message and you can sway people to do your bidding. That's one of the reasons we have freedom of the press. It keeps the people in power from controlling the message and staying in power forever. We see this type of manipulation regularly in other countries.