How far is it true that none of the great powers involved in the Korean War had expansionist ambitions?
This is an accurate statement. The only country involved in this war that truly had an expansionist agenda was North Korea. It is true that some American leaders would have liked to expand, but this was not the main thing on their minds.
The great powers involved in this war were the US and China with some Soviet involvement. None of these countries was truly bent on expansion. The US was trying to repel the North Korean invasion. China only got into the war when it felt that the US forces were becoming a threat as they neared the Yalu River. The Soviets were backing their communist allies but all they really cared about was not letting North Korea get destroyed. In this way, the great powers were all really just trying to maintain the status quo that had existed before the war.