At the risk of revealing some rapidly silvering Cold War roots, I am both amazed and unsurprised at how many high-ranking politicians (and some military) do not and did not know about Perimeter. Then again, many "leaders" over the years have not gotten the word on a number of things they should have known about. Part of this was incompetence; part was bureaucratic inertia; part was deliberate, with some blocking info for political motivations; and, part was something for which I'm still trying to find the words. And, yes, secrecy and deception plans did sometimes work. The bureaucratic side of things was why Reagan had a "kitchen cabinet" of advisors on Soviets, science, and some other topics of note.
That said, there were some outside the Soviet Union who knew about this early on. If you don't know about it, you need to read the article. It gives as good a description as you are likely to find in the open, and the theory/gamesmanship described hits some good points. Perimeter was a way to buy time, and not just your prototypical Hollywood doomsday device. That, however, does not negate that it was a doomsday device.
To understand the relevance the system (still operational) has today, you need to look not just at the formative years/Reagan years. You need to google the terms Norway weather rocket Russia and false alert. You might want to consider a purely hypothetical situation (one John Donovan might recognize) of what might happen if Islamicists overran (or were given control of) a weapons depot in a contested area of the old Soviet Union. Suppose this depot may have also contained "special" weapons and that once positive control was re-established it is discovered that no one can tell if any of those special weapons are missing or not. Or keys. Can you imagine a Soviet Premier contacting NCA with a request that the U.S. not launch on boom, and that the Soviets will not launch on boom either -- especially if said boom takes place within the Soviet Union?
Think about that hypothetical in terms of Perimeter. Think about the changes that have taken place over the last 20 years: the rise of Islamic terrorism (or Islamofascist or whatever PC term is acceptable to you); the deterioration of U.S.-Russian relations; and, internal changes to the Russian political landscape.
The sad fact is that leadership (here and elsewhere) is often briefed on what they want to hear, or what others want them to hear, and not on what they need to hear. I long ago gave up on having top leadership that got that others don't think like them, or having them even begin to have a tiny grasp of the mores of that culture. That's the suck, and it has to be embraced.
What we can't afford is to have leadership (here or elsewhere, but here especially) that is not briefed on, and understanding the implications of, things like Perimeter. Kudos to Wired and Nicholas Thompson for an interesting and needed article.