I'd say the last 50% is the easier part to imagine.
The odds of a stray missile randomly landing near hikers, while possible, is going to be millions-to-one considering all the potential impact zones it could have landed. But the focus of a case of mistaken identity, a 'friendly fire' incident at night, with victims under the canopy of trees, when a tired helicopter crew have already been out looking for escapees for most of the day, is much more likely.
There was only 8 hours of available daylight to search a region, and I think they would tend to concentrate on escapees being on the move then, and seeing them in the snow between forests and on passes, and when darkness fell at 4:29pm I can't see them knocking-it-on-the-head and would instead continue until the evening, adopting a new approach of anticipating escapees seeking shelter in forests and lighting a fire.
They may even have followed the hiker tracks to the forest, and the moment they saw a fire their adrenaline would pump and they'd convince themselves "this is them". If the hikers ran or hid, even from fear, it would further suspicion from the air. Some warning shots may have been fired, followed by ordnance, perhaps involving gas, if wishing to explain burns and breathing problems, something designed to subdue.
The next day they'd return and realise they have killed hikers, explaining the military knowing about them before the official alert was given. Had this been a group of Mansi, or Russian hunters, rural people living off grid, then nobody would care enough, they could probably get away with admitting to it. But this was a group of townies, "a bunch of kids"; uni students, their young mechanic friends, and a war veteran, so it would require special handling - a cover-up, rather than admitting to a tragic case of mistaken identity. The secret would die with the helicopter crew not only because of the secrecy required, but because through shame they would never want to publicly admit what they did.
To me, this photo, an enhanced and colourised version of what is the clearest image from Semyon's film, is the smoking gun of the DPI. I have every confidence that if, away from this forum, 1000 people were randomly asked what they thought it was, and perhaps told it was taken at night up a mountain, very few of them would suggest it's a shapeshifting glowing entity, 'fireorb', fireball, ball lightning, UFO or other rare phenomena or folklore, and will instead suggest a headlight of a helicopter or possibly a ground vehicle.
That's because the light has a distinctive, vaguely familiar shape, and is of uniform luminence, usually achieved with a reflector around the bulb. If they looked further and noticed how the beam shines down through cold air they may logically decide on a helicopter. Because only the Soviet military had access to helicopters in 1959 this then places them at the scene, and Semyon's objective in attempting to take photo's of the night sky with his rudimentary camera, in this theory, would be to try to leave clues as to what happened to them.
He would not flee his tent in panic without taking the tools to survive away from that tent, if sited on a mountain ridge, instead grabbing only a camera, but that is something he would be more likely to grab if their tent was already in the forest, the place they supposedly travelled to, when the incident unfolded.