I'm also aware that back in 1986 not everyone was walking around with a camera in their pocket.
Are you really?
It goes a bit further than that, my friend. Of course lots of people did carry cameras but usually for a reason. One didn't walk around with a camera 'just in case' or 'for the fun of it'. You don't do that with 'wet' cameras. Almost nobody had a mobile phone back then, and the few mobiles that existed didn't have cameras. A mobile in those days was huge. You needed a backpack to carry one. Literally.
However, the above is about the Western world, where people had the money and the freedom to walk around with cameras. Do mind that walking around with a camera near a nuclear facility in the west was and still is severely restricted.
Now we have a look at the USSR. A lot less people carrying cameras there. For two good reasons: USSR citizens had much less spendable income and the state wasn't particularly keen on people taking photo's without a good reason.
Next, we're talking about a nuclear facility in the USSR. That's a strategic asset of national importance. Photography there was absolutely forbidden. Merely walking around with a camera would get you arrested on the spot. Immediately. Even if you worked there, you had to have a bloody good reason to bring a camera to work. "Igor has his birthday party" was not a good reason.
Technical video camera's did exist, but they were both large and very expensive compared with modern equipment. So it is extremely unlikely the actual event has been or could have been taped.