Question: “although Johnson realized what was going on, he played his allotted part” question.

[Dirty Duck]

President Johnson knew the purpose of the S3 Program but he still did what the Patriots intended for him to do rather than fight against it.

It's worth noting that this is potentially only Ocelot's idea of the S3 Program, the Solid Snake Simulation, in which Johnson is a stand in for Baker-who dies but not before imparting the knowledge on how to stop the nuclear launch.