I was under the impression that Kirk's lie on the report was the problem. The fact that this indicated to Pike and the other admirals --but mostly Pike I suspect--that Kirk was not responsible enough to own his command decisions and that perhaps his command crew did not work well together. They needed more experience. The fact that both Kirk and Spock were still going to serve in a command crew position indicates to me that it was felt they needed some training but were thought capable officers.
There were a couple of issues.
1) Spock and Kirk decided, together, that the Prime Directive would be suitable preserved if the native population of Nibiru did not see the Enterprise, her crew or any support vessels. They enacted a plan based on that interpretation of the PD. The plan went ary and Kirk decided to break cover to save Spock and expose the Enterprise to the native population.
2) Spock filed a report detailing what happened on Nibru. Kirk filed a report filled with damn dirty lies.
Even if the plan succeeded, Kirk would have still run afoul of Pike because Spock's report would have been about the successful preservation of life on Nibiru while preserving the PD (from his POV.) Kirk would have still filed a report filled with damn dirty lies and Pike would have still had the same reaction he had on screen.
Pike didn't agree with Kirk and Spock's interpretation of the PD, full stop. That the plan failed and Kirk was forced to expose the Nibirans to the Enterprise is beside the point.