> there have been reports that Russian pilots flew North Korean MIGs in air-to-air combat with U.S. planes
Stalin was careful enough to enlist pilots as "volunteers", suspending their official service in Soviet Army for the duration of mission.
It's not quite as black-and-white as that, as illustrated by the history of the second half of the 20th century: The U.S. and USSR engaged in several proxy wars (Vietnam, Afghanistan, arguably Central America), but never came close to nuclear war.
(Neither the 1962 Cuban Missile Crisis nor the 1983 Able Archer scare involved a war, and the Korean War of 1950-53 was apparently started on Kim Il Sung's own initiative to the surprise of the USSR, although there have been reports that Russian pilots flew North Korean MIGs in air-to-air combat with U.S. planes; when China came into the war in November 1950 it wasn't yet a nuclear power.)