This particular document doesn't even touch on more advanced tings like this so it makes sense to leave it out and keep it to the simplified but still correct statement: One space, nothing else. That's it. If you do something else you are wrong.
It's just a typographical shibboleth, nothing more.
Seeing as the original article always tells you how to do things in Word, it means exactly that. Any system that is not not WYSIWYG will have no problems here, Word does. And since most people use Word, this is relevant. It doesn't matter that TeX doesn't take it into account, because this is not primarily written for TeX users. TeX does many of these things, but it is not what most people use, especially those who do not know anything at all about typography.
To emphasise what I said above: the book is passing off a didactic point about authoring (yes, many newspapers and publishers want their journalists and authors to follow the one-space rule in their copy) into a simplistic rule of typography, one which happens to be meaningless in many contexts and is based on fallacious reasoning.
If I put two spaces after a period, am I wrong, or simply differently habituated from people who learned keyboarding in the electronic age? And even if I am objectively wrong, I maintain that my wrong is less egregious than the wrong committed by a program that cannot accommodate that very well-documented and widespread typing error.
In the TeX source code, you can put as many spaces you want between words and sentences, TeX does not mind and will produce the exact same result.
So in the context of TeX documents, "One space is correct and nothing else" is either meaningless or false.
One space is correct. It's so correct, TeX will even automatically strip spaces away if you make more than one. (Happens on the web, too, by the way.)
For abbreviations, you should explicitly insert a space control sequence (\<space>) or a non-breaking space (~) after the period.
Just in case that sounds too simple, there is an exception for initials: `P. G. Wodehouse` is treated the same as `P.\@ G.\@ Wodehouse`. If you want to cancel this, prefix the period by `\@`.
This kind of thing makes Latex a hard sell to a general audience.
See http://latex-alive.tumblr.com/post/827168808/correct-punctua...
I think if you think about it, you'll realize this is just TeX agreeing with what he said about one space.