The podcast When Diplomacy Fails has a series on the Korean War that proposes, in extreme brief, the following narrative of how the Korean War broke out:

1. Stalin wanted the North to invade the South in hopes of creating a quagmire that would suck in China and hamstring Mao's efforts to create a strong and stable regime that was substantially independent from the USSR. In the worst case scenario, the North is too successful and succeeds in conquering the South too easily, scoring a PR win for communism internationally.

2. Truman hoped for the same war to break out, but instead to justify a massive military buildup that could be used to counter the Soviets more broadly. The attack could also justify more aggressive anti-communist posturing in general, on account of such a war being a communist war of aggression.

3. Stalin actively encouraged the war to break out by supply the North with the materiel needed to fight the war and by putting in the work to convince Kim Il-sung he should launch the war.

4. Truman's government also encouraged the war by intentionally keeping the South undersupplied with arms and troops, in hopes of making it appear as an easy target. The Americans also turned a blind eye to a military buildup in the North that would have been impossible for American intelligence to have missed and sent intentionally weak and confusing diplomatic and public press messages regarding American defense commitments.

So, in summary, the story is that America set up the South as bait and the North took it, given that they rather wanted to take it anyway.

My question is simple: is this narrative true? The podcast acknowledges that this is something of a revisionist narrative. Some of the evidence it adduces is reasonable (comments on various internal US strategy documents) while other strikes me as less persuasive (speculation about what was an intelligence failure and what was a matter of intentional ignorance). I do not know enough context to fairly judge the matter, however, and am hoping some among you may be able to tell me more!