I'm familiar with Spetner's arguments. The problem in bried is that he offers a measure of information, but only uses part of it and keeps changing how he calculates the information change so that he gets the result. For instance in one case he measueres specificity against one compound. In another he finds that doing that doesn't give the result he wants and insistes on using three compounds - without explaining why or how the extra two were chosen, why one was good enough in the previous example or why three is enough this time. In another case he uses an entirely different and arbitrary measure (based on the size of sets) instead of looking at specificity at all.
Really it looks to me as if his main concern is to get the results he wants. He doesn't do a full measure of information by his own list - only an incomplete calculation of one aspect (and in one case not even that) and isn't even consistent in how he does that.
(And since you've got his book I'll mention that some years ago I got involved in a discussion of his argument about the probability of speciation - where he made a big mathematical blunder).
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