I have two problems with this "argument."
The first is that it assumes an Enlightenment positivism in man's knowledge, as though we can actually reconstruct things like history and origins clearly enough to determine if the Bible contradicts itself, contradicts science, contradicts history, etc.
Of course, I can affirm that it does all of those in terms of its human assumptions and language, but there is a mistake being made here nonetheless. When you learn so much information and have been corrected so many times by new information and new ways in seeing the information, this usually makes you humble by causing you to realize that you probably don't know as much as you think you do. In fact, I've often argued that genuine knowledge of the world, apart from revelatory knowledge, is an impossibility. But this is especially true of metaphysical and historical questions.
But unfortunately, with some people, when they are finally given that PhD by the Wizard they suddenly think they're studies are capable of producing omniscience. Of course, everyone realizes this is bogus, even those who do it, but their rather double-minded in that respect.
Second to this, however, the analogy is false, precisely because the question cannot be determined based upon the interpretations of the data through naturalistic presuppositions without begging the question. Instead, because the issue of origins, or inspiration and inerrancy, is ultimately a faith question, we should have two bunnies looking at a painting by an author and interpreting it as a sort of Rorschach experiment.
The analogy given by McGrath assumes an objective view of the evidence and a sufficient amount of knowledge/data in order to objectively piece that data together.
Instead, this sort of mockery of one's opponents in an attempt to show how stubborn and dumb they are is just partisan politics. I could have easily set the same scenario up where, even though the picture was matching up really well, the errantist would continually find contradiction and try to fit the pieces in the wrong places so that it looked nothing like the picture on the box--thus fulfilling his own preconceived idea of the text. But these adolescent games are unhelpful and ultimately convincing (and funny) only to the bitter apostates who want to demean their critics.