I don't know what's so hard for you here to understand to be honest. Genuine grievances did exist, but they were exploited and fomented artificially by the CIA. Both things happened at the same time. That's exactly how the CIA operates.

The student movement, the factory strikes, the elected workers' councils, all of that is documented. They had real complaints about living conditions. But real anger doesn't mean the uprising wasn't steered and fomented externally. The CIA and Radio Free Europe agitated for unrest, amplified it, and pushed it toward insurrection. They advised insurgents on how to build barricades and fight Soviet troops. They dangled the false hope that the West would intervene. Dulles saying "we encouraged them but we cannot save them, the propaganda value was enough" tells you everything you need to know about this uprising. They never intended to help, but they wanted a spectacle for anti-communist propaganda and an opening for intelligence expansion, so they helped create the conditions for one.

So the question isn't whether grievances were real. It's who exploited them and whose interests they served. The CIA fomented the uprising to advance its own Cold War agenda to manufacture the insurrection. That doesn't negate the legitimacy of the complaints in any way. It just means the uprising itself was not the organic expression of the Hungarian people that you're making it out to be.

As for Béla Király, you're right that the timeline doesn't support him being a CIA plant before the revolution. He was arrested in 1951, sentenced to death in 1952, and only paroled in September 1956. The CIA relationship came after the revolution, when the Hungarian Freedom Fighter Federation was founded in New York in 1957 with Király as its chairman. But none of that actually matters here because the CIA didn't need a single agent inside to steer the uprising. They had Radio Free Europe, they had leaflet drops, they had a whole information warfare apparatus in place, the operation of which is explained in great detail in the book I linked you. They didn't need to train militants in the mountains when they could push people toward insurrection through propaganda.

The weight of historical evidence isn't on the side of a reactionary coup in the sense that the grievances were fake. The uprising itself was exploited and fomented artificially by the CIA. Both things are true at the same time, and the real discontent of Hungarians was used to serve American imperial interests.