Sounds like a load of cow manure to me. I love Penn&Teller, but frankly, much of their BS episodes are BS in their own right. They really needed to fill those seasons and when they run out of arguments, they start shouting.
A militia is, by definition, not a standing army. It is formed by civilians. Here's a definition: "Militia: a military force that is raised from the civil population to supplement a regular army in an emergency." Here's another: "a military force that engages in rebel or terrorist activities in opposition to a regular army." There was a militia at the time, they were civilians. They bought their own weapons. That was considered the right way to defend the country. For the people, by the people. The standing army came later, and it wasn't called a militia.
Even on linguistic grounds, the argument doesn't make sense. The amendment reads: "A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed." Now let's enter a definition of militia in there: "a military force raised from the people". Now the argument reads: "A well regulated military force raised from the people, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed". You're sure that the first people are not the same as the second people? Why would the people need to fight the people? Were the founding fathers advocating permanent civil war?
Your argument is, indeed, bullshit.