It is perfectly possible, and that is all I need to know; all it requires is the right set of biases in the system. It is trivial to demonstrate a set of biases that will work, and given the thermodynamic chaos of the universe it is rather obvious that those biases must be occurring regularly.
The real fallacy is attaching some special significance to DNA. It could have been any number of other compounds that share every useful property of that chemical (and there are others). Just because you picked the winning numbers for the lottery does not mean there was something special about the numbers that you picked. In the case of the universe, the number of drawings that have occurred is so large that all probable chemical pathways have already been drawn as it were. DNA is a "probable" pathway in this sense. If you look at all conceivable combinations it is improbable, but if you only look at the favored chemical pathways (which is the only valid way of looking at it chemically) the odds become very good.
"It is perfectly possible, and that is all I need to know; all it requires is the right set of biases in the system. It is trivial to demonstrate a set of biases that will work, and given the thermodynamic chaos of the universe it is rather obvious that those biases must be occurring regularly."
Nonsense. That's like claiming that a fully programmed and constructed space shuttle will pop out of a volcano with U.S. marking on its wings one day given enough time and enough universes.
The fallacy in your logic begins with the idea that every level of ordered complexity can be created naturally, but Nobel Prize Winner Illya Prigogine conclusively destroys that argument in his tome Order out of Chaos.