The author of that book—it’s actually his autobiography—is Stephen Fry, a British comedian, actor, writer, and activist. I’d say his views about English grammar are quirkish but charming, fun to read, and sometimes devilishly spot-on (Check him out in the YouTube video
“Stephen Fry’s Kinetic Typography” by clicking the indicated link). But as to the assertion that, as you quote him, “the apostrophe in ‘it’s’ had only been there to avoid confusion with the elided ‘it’s,’” I frankly don’t know what to make of it. What I know is that “it’s” is used only as a contraction of “it is” or “it has,” as in “It’s a rainy day today” (Unelided: “
It is a rainy day today”) and “It’s been a lovely evening” (Unelided: “
It has been a lovely evening.”) The elided “it’s” is unique in that while every English noun or pronoun with an apostrophe-“s” indicates possession, “it’s” doesn’t. “It’s” only works as a contraction of “it is” or “it has,” so I suspect that Stephen must have had something in mind—perhaps a zany punch line that never got written in that book—when he made that curious assertion.