Teribus, it is FACT that the Allies invaded North Korea at the insistence of MacAthur when Truman was happy for the Allies to stop at the 38th parallel. It is FACT that the Allies managed to get as far as the Yalu River which marks the geographical and political border with China. It is FACT that the Allies were ignominiously thrown back to the 38th prallel by vastly superior Chinese forces.
The only reason that China did not go further was because her supply lines were becoming dangerously over-extended.