There's a semi-comfortable middle ground here that I'm reluctant to get into for reasons of keeping things fun for everyone.
Bottom line: yes, you can cross the streams and alter the timeline. But, the game is also trying to determine results on the basis of the plate appearance. If you dig into things far enough, you can see how this makes complete sense, how it allows the human GM to be baseball-like in their approach (which is fun), and how it warps things in ways that don't make sense in some cases.
Regardless, the game does not predetermine a winner.