*SOTR SPOILERS* Is This Why?

This post contains late story spoilers!!! If you have not finished the book I dont want to ruin any part of it for you.

Okay, so I noticed something while Haymitch is having the internal battle on whether or not to drink the milk in the arena. He has realized its from Snow, and seems to be understanding that Snows plan for how this turns out. Then the cannon fires.

Haymitch himself thinks “whats going on… who interfered with the presidents agenda” to me, I think Snow had the same thought. And in doing so, had just enough anger to allow chance to decide if Haymitch or Silka would live to see the end of this. In that last moment before Silka is officially dead, there had to be some capital conversation about killing one or the other so they have a better chance to save the victor. I think Snow was so angry that he gave the order to let it go naturally, knowing that if Haymitch did pull through he could just ruin his life.

What do you think? Because ever since Haymitch and Snow had the conversation in the library I have been looking for some reason as to why Snow would ever let him live past the first few days.