Good question! I propose as follows:
Firstly, you agree that the oil having burned 8 days vs 1 was a definitely a miracle, right? Second, "What is the purpose of a miracle in the first place?" I ask. Well, quite obviously, the most basic purpose of a miracle is to show us that God is currently watching us, cares about us, and has control over everything that is happening. Okay, now here goes the answer.
Once God clearly indicated the three aspects of his providence listed above, through the performance of the obvious miracle of the burning of the oil, that naturally directed the Nation of Yisrael to look back at the recent events and see things in a new "light"! A "Light of Miracles" to be precise. They now naturally saw how the "Victory of War" wasn't just a "Lucky Victory" and they further realized that the "Finding of the pure, sealed flask of oil" wasn't just a "Lucky Find"! In truth, I assume that this is the effect that miracles are supposed to have on us. Obvious Miracles are supposed to lead us to see God's intervention even in those things that we might have taken for chance! I hope you like this answer.
Edit: I just want to add that this might be the reason why we light the Menorah backwards (4,3,2,1) The Neis is about looking "backwards" into the past to see God's miracles.