You are absolutely right, but I don't think the philosophy of science demands that you actually follow the scientific method during discovery mode. What it says, though, is that if you discover any scientific knowledge, its discovery process must be castable in the way of the scientific method. Meaning, when someone else checks or replicates your result, they can actually follow the four step process, and recreate that same knowledge.
Science more than just a collection of facts, is a description of a set of experimental processes that recreate those facts. Which is where the authority-lessness power of it comes from.