I think the MSM runs the Democrat Party and can do or say anything they want. They run the USA and not the Federal Government which is just the executive branch for the MSM. 95%+ of the deep state bureaucrats are Democrats and by default under the control of the MSM.
I view it as a sort of independent divisions of the same company. All have the same end-goal, each responsible for a different product. The press, the politicians, the bureacrats, the schools, the entertainment industry, the courts, business interests, and even the churches are in on it.
There is a synergy there. The MSM and politicians reinforce what the schools teach.
"Which branch is taking the lead" varies depending on where the talents lie. Right now the politician division is weak, and the IC is using the MSM to drive the action.