Are you sure that you are not referencing the Penguin Guide to Punctuation?
In any case, although the The Chicago Manual of Style (17th ed.) has a different opinion on the punctuation of names that end in s, it actually says the same thing about their pronunciation.
Chicago, 7.18, says:
Words and names ending in an unpronounced s form the possessive in the usual way—with the addition of an apostrophe and an s (which, when such forms are spoken, is usually pronounced).
Descartes’s three dreams
the marquis’s mother
François’s efforts to learn English
Vaucouleurs’s assistance to Joan of Arc
Albert Camus’s novels
And Chicago, 7.19, says:
Classical proper names of two or more syllables that end in an eez sound form the possessive in the usual way (though when these forms are spoken, the additional s is generally not pronounced).
the Ganges’s source
So, regardless of whether the non-possessive form of the name is pronounced with an s or not, the possessive form of the name is pronounced with a single s.
Note, however, that Chicago qualifies its statements, saying usually pronounced and generally not pronounced.
Since there is even less of any formal guide for pronunciation than there is for grammar, pronunciation is generally left to the whim of how groups of people actually speak—and there will always be variations from one group of people to another.
Even those dictionaries that do provide pronunciation guidelines are unable to properly mirror all of these variants.
As for myself, let's take Socrates's. Going against the "rules" of both Penguin and Chicago (assuming that this is not one of those exceptions), I actually pronounce it as "Socrat-eez-es."
On the other hand, I follow the "rules" and pronounce Ulysses's as "Ulyss-eez."
I can't say why I am inconsistent in this way. That's just how I've always pronounced those two possessive constructions, and doing it differently would simply sound strange to me.
No doubt both Penguin and Chicago are simply mirroring what they've seen to be the most common way that people speak—and then mentioning that as a guideline. But not everybody does speak that way.
As for why, who knows? Pronunciation (as spelling) will almost certainly change over time. It's simply determined by whatever is the most comfortable to each person at any given time—and all that can be done is to record current usage.