This is part of what drives me mad about 'the debate'. Both sides consistenly obscure the distinction between the three meanings of 'evolution' I mentioned in my semi-defense of Behe. The first (allele and phenotype dynamics) is simply an observable fact; the second (common descent) is plainly a solid falsifiable (a single organism with a different system of codons would suffice) scientific theory and every observation to date supports it; the last (neo-Darwinism) is the one I'm not even sure manages to be a theory (though once one vacates 'random variation' the way the definition at http://evonet.sdsc.edu/evoscisociety/what_is_evolution.htm does) and leaves natural selection as a tautology (rather than 'so formulat[ing it] as to be far from tautological') which seems to be the tendancy, lest a falsification of a particular such formulation give aid and comfort to religious obscurantists, it's a 'fact' too (but not a very interesting one), provided one drops the insistence on its completeness and sufficiency as an explanation.
Common descent is not what it used to be. It is no longer thought by the mainstream of biological science that a single organism gave rise to all life. Which, by the way, if so, casts a serious measure of doubt on the single-system-of-codon falsification notion.
Ultimately, one would like to see a path from organism A to organism B by mutation and natural selection, with every step in between a viable organism. I'm confident eventually we will be able to reconstruct such a pathway, though we simply don't have the experimental capability of doing it yet.
I am at a loss as to why we are "abandoning" random variation, and I don't believe I can cut through this thicket of verbiage to get at it. But I am not quite ready to toss it in the trash bin, and I don't believe most biologists are, either.
We obviously have random variation to provide a base population upon which selection operates. We are recently noticing that our centuries-old assumption that the randomizer had a uniform initial distribution before selection started whittling on it, might have been off the mark.