The distinction that needs to be made here is that between a genuinely simple
explanation and a simple
description of a complicated one. If the two aren't separated, all we have is a contest of abridgement.
Genesis is simple if you leave out all the details. As soon as one attempts to find mechanisms that would cause events to take place as the book describes, things get vastly more complicated, more so than "natural processes that we observe today, including random mutation and natural selection, produced the variety of life we see at present and in the fossil record." Witness gap theory, appearance of age, drastic changes in light speed and radioactive decay, vapor canopy, vegetation mats, "kinds" that replace anything from a species to a family as needed while hyperevolving at impossible speeds (and then slowing to rates compatible with old-earth evolution), et cetera. Simple? "So complicated they can't be assembled into a coherent whole" is more like it.
Evolution is simple, but the beings on which it acts are fabulously complex. To understand the process, we therefore must dig into the complexity or resort to argument from ignorance, which is what the wiz seems to advocate. I would prefer to live without all the answers than simply assume an easy explanation and then shut off my brain.