The claim that DNA is irreducibly complex is just as groundless as every other claim of irreducible complexity.
Creationist information theory is Christian pseudoscience at its finest:
"Creationists, in an attempt to coat their myths with a veneer of science, have co-opted the idea of information theory to use as a plausible-sounding attack on evolution. Essentially, the claim is that the genetic code is like a language and thus transmits information, and in part due to the usual willful misunderstandings of the second law of thermodynamics (which is about energy, not information), they maintain that information can never be increased.[10] Therefore, the changes they cannot outright deny are defined as "losing information", while changes they disagree with are defined as "gaining information", which by their definition is impossible. Note that at no point do creationists actually specify what information actually is and often (even in the allegedly scientific case of complex specified information) will purposefully avoid defining the concept in any useful way. The creationists tend to change their meaning on an ad hoc basis depending on the argument, relying on colloquial, imprecise definitions of information rather than quantifiable ones -- or worse, switching interchangeably between different definitions depending on the context of the discussion or argument.
The deliberate conflation of the totally unrelated concepts of thermodynamic and informational entropy is, while an obvious flaw in the argument, a flaw that the creationists' intended audience is less likely to pick up on, so it remains a popular argument, as seen in Ken Ham's... debate with Bill Nye at the Creation Museum."
http://rationalwiki.org/wiki/Information_theory#Creationist_information_theory
Irreducible complexity is a classic example of a God of the Gaps argument. Every time science exposes more of your religious bullshit to be wrong, you improvise new,
ad hoc reasons why your silly claims might still be true.
