A better analogy might abstract away the merits of copyright infringement, and focus on who got punished for that infringement. Maybe something like: "Imagine if the government shut down Walmart because one of its customers was caught handing out ripped Beyonce CDs."
I don't think it's a correct analogy, since the copyright infringer isn't doing any possible (or perceived) damage to Disney. I think the pattern should be: "Company X gets shut down because one of its customers broke Law Y at the expense of Company Z".
And the best Company X I can think of is a sports franchise. (A customer base that is too large to monitor in real time, and that forms a community that would get shut down along with the business.) So what are Y and Z? I don't think they even have to differ from the reality. "Imagine if the government shut down the Boston Red Sox because one of its fans was handing out ripped Beyonce CDs." Or maybe the fan should be selling fake Rolexes, since that probably actually happens.
Unfortunately, while you may stumble upon an analogy that describes what could happen to some "poor business", they will all be disingenuous because your analogy leaves out the scenarios that Uncle Art would probably want to see action taken on.
What is happening in many cases is the Boston Red Sox gave the guy selling the Rolexes a booth to sell them in, and directed people searching for "Rolexes" to his booth. The Red Sox hung up ads along the way and made money from all the people who walked past those ads on their way to get Rolexes. Someone reported those Rolexes stolen, so the Red Sox kicked the guy out with no penalty to the guy or the Red Sox, and then let some other fake watch seller setup shop in the same booth. This kept happening for years, and Rolex had to lay off 4000 people, while the Red Sox made a killing.