Occam's razor is that principle that is often understood being that "among competing hypotheses, the one with the fewest assumptions should be selected." To put it another way, all things being equal, simpler explanations are generally better than more complex ones.
Needless to say, Occam's stranglehold on how we understand God is rather strong. It is how theologians talk about the mystery of something like the atonement but we teach it by way of 3-4 theories. Or we talk about the mystery of the trinity but boil it down to that like an egg or water (see here for a silly little video on why those metaphors are "heretical")
Christians try our very best to try to communicate to the world the vast mystery of the creator of the world can be understood and, the most simple explanation tends to win out because we all prefer Occam to Hickan.
This sounds weird but the point that Hickam was trying to make is that patients can have many different symptoms that are unrelated and cannot be diagnosed under one simple, elegant explanation for instance Saint's triad.
Christians are not unlike other people in the world in that we desire a simple answer to the questions of the world. We long for someone to just tell us why something is the way it is or what we are supposed to do. We willingly accept someone citing scripture at us, giving us a response that is so tight that is might as well be a package tied up with a bow. The answer looks nice, it is elegant and makes sense. Classic Occam's razor.
The reality is, if Occam's razor does not hold for medicine then it surely does not hold for theology. No matter how elegant the answer may be, when we are talking about God - it is never that simple. Cite me the chapters and verses, point out the creed, quote the theologian, articulate the church council, all of these actions are efforts to prove the razor.
The preachers and teachers that give you a razor's answer provide great comfort. I am a razor pastor myself. However, in my more antithetic moments I will share that I don't have the simple answers. And in my even more truthful moments I will share I don't have the simple answers because no one has them.
Simple answers don't exist when we are talking about God. They never have.
Hickam's dictum was introduced to me via this wonderfully fantastic podcast episode of "Reply All" - Boy Wonder.