I'm afraid that only one confused... is you.
The supreme question for this thread is really whether DNA can self-form naturally, in an unaided, unintelligent, primal, "random" environment.
In this sense, "random" infers that an intelligent intervention is not "loading the dice" (i.e., loaded dice aren't random).
When a programmer creates a program, her code is not "random". Said program was created through intelligent intervention, not naturally, not randomly.
Of course it can. There is nothing special about DNA. Nothing special at all. There are other classes of organic chemicals that could have formed the basis of life and exhibit the same basic properties.
In this sense, "random" infers that an intelligent intervention is not "loading the dice" (i.e., loaded dice aren't random).
You don't need "intelligence" to load the dice because in the real world the dice are already heavily loaded by the basic rules of the system. This is one of the great fallacies that I see pop up time and again. Nothing in chemistry is random in that there is an equal probability of all outcomes. Thermodynamics (in its very broad and mathematically ugly sense as it applies to real chemistry) strongly biases chemical interactions in a thousand different ways. Some of these biases constructively reinforce each other while other biases create destructive interference with themselves. The notion that organic chemistry is a roll of the dice is absurd and naive. But it isn't intelligence that makes this so, it is the complex rules of the system. Given any system with lots of thermodynamic chaos, you'll get every odd chemical under the sun in at least small quantities, so complex chemical accidents are probable if they are favorable under the given conditions. This is why even under the most controlled environments organic chemical synthesis tends to produce a bunch of complex "other" compounds in the process. Thermodynamics drives the complexification, and the chaos of the system ensures that some of the side-effects are indeed "complex".