Are people forgetting that the USSR lent support to North Korea and China lent support to North Vietnam-- at times when both those countries were nuclear powers? It has been demonstrated several times throughout the past 70 years that nuclear nations can be brought into conflict (however indirectly) without resorting to using WMDs.
Neither of those are serious. Neither the USSR in 1950 nor China in 1967 had nuclear capabilities of destroying the world or even the US. A nuclear war over Korea would have likely resulted in an actual US Victory even if the USSR responded.
The fact that the destruction of the planet wasn't a possibility would have made the use of nuclear weapons more likely back then than it is now.