The circumstantial evidence for a military presence is reasonably strong.
Unless you believe in alien spacecraft, or ball lightning, the orange orbs seen hovering in the night sky, lasting from seconds to minutes, could be helicopter/s, where a search light appears orange at distance, or amber lamps were deployed for higher contrast in snow, as with car headlamps in alpine regions. Rotor noise would not be heard by witnesses at distance.
Mention is made of swirl marks seen in the snow near the tent, which could be caused by the downdraft from the rotors.
It's reasonable to assume that, with the camera found around his neck, Semyon took his night photo's that night, and the gist of them shows a bright lamp of distinctive shape, and one photo of a 'plane' looks suspiciously like a Yak-24 troop carrier, down to the particular shape and lines of the cockpit windows, the twin rotor stacks and other key features. Semyon's rudimentary camera would only be capable of taking images of relatively stationary objects at night without blurring (shutter speed versus aperture setting).
Because snowmobiles, 4WD and quad bikes were not available then, and would leave obvious tracks if used, the only conceivable way for the military to get there at night would be by helicopter. The timely coincidence of escapees in the region, some of whom may have been of high political value, provides a reason.
It's possible the helicopter dropped flares to get a better look in forests, explaining the burning to some tree tops.
It seems obvious the group felled their tent and covered it with the trench snow spoil, and because logically they wouldn't choose to do that when leaving without first retrieving all they needed to survive, this suggests there was a delay between felling and leaving, and that all adds up to hiding/staging the tent as abandoned, with hypothermia setting in by the time the coast was clear.
I believe the hikers would pitch their tent where they did to avoid the escapees they would have learned of at Vizhay, and then found themselves a little too conspicuously in the middle of a search zone at night.
The next day the military would continue their search, see the bodies on the pass (before snowfall covered them), and either land or abseil someone down a rope, the evidence of this activity hidden by the later snowfall, and turn the bodies, determine they were hikers, and make the connection with the 'abandoned' tent. It would be played to this day as though they were never there, because people would either blame them, directly or indirectly, for causing their deaths, or ask why they did not rescue them if they were searching that area and the hikers were in some other difficulty.