I think he only meant that under our current laws, nuclear armaments are not available to the average Joe regardless of what red-tape they're willing to wade through, as opposed to some of the other items being discussed, like tanks or planes, etc. I don't think he was arguing the right or wrong of the matter.
Since finding the line in the middle is an exercise in perpetuity, let's explore it from the extreme: nuclear weapons. Now for The Question: Are there any reasons as to why I wouldn't want your average citizen to have an operational nuke?
It's not that I think there's a high chance of them doing something heinous with it, like driving to the center of a major metropolitan area and pushing the button. It's that the propensity for such catastrophic damage outweighs the tiny risk.
More to the point:
Probability: Let's call it 1 in 1 million, or 0.000001
Cost in lives: Let's call in 1 million.
Cost in dollars: Let's call it $10 billion
Thus, the Net Probable Cost of allowing this would be: 0.000001 * (1,000,000 lives + $10 billion) = 1 life + $10,000
This doesn't sound very extreme, does it? Compared to what we carry, any one of us could go loony, cost someone their life and rob their family of at least $10,000, right?
These two scenarios, however, cannot be compared using Net Probable Cost alone, as they have vastly different "worst-case scenarios." In the case of an armed gunman, a worse-case scenario involves dozens killed and dozens of millions in lost monetary value. In the case of a single rogue nuke,however, a worst-case scenario involves millions killed and billions of dollars.
Quite frankly, the risk is too high, one I am not willing to take to support someone's self-acclaimed right to nuclear arms. Regardless of what the Constitution actually says, our Founding Fathers couldn't envision nuclear weapons in that day and age, as the destruction goes many orders of magnitude beyond any conventional arms.
Let's go science-fiction and suppose some kid invented a way to quench our sun...
So yes, there is a line, but it varies for everyone.
But if you want a .50 cal perched on your porch step, go for it.