I was an Air Force crew member on a special mission Herk (EC-130E) back in the 90s...flying over Bosnia, we sometimes climbed to 30-31K later in a sortie, after burning off enough fuel.
Maximum service ceiling for a C-130 is 33K; ceiling for an AN-26 (twin-engine turboprop versus four engines on the C-130) is about 24K.
Hard to believe they could “mistake” a 777, crusing at 34K and 500 kts of airspeed for a turboprop flying 10,000 feet lower, and at a speed of around 220 kts.
You would think the radar system would have given them some type of clue. Speed. Altitude. Etc. Apparently it did not have friend or foe identification capabilities.