Interestingly enough, although the stress from nominative plural to genitive plural does not change, both words (сторона and война) have a change of stress between singular and plural. Is it possible that the source KCd refers to is actually referring to stress changes between the singular and plural forms of the word? I suppose it is possible, but doubtful. I get the impression КСd may actually be quoting from it directly. The source isn't mentioned, so I can't try to find a copy online. (Even if it exists, it could very well be in Russian, not a bad thing, but my Russian is not nearly good enough for accurate interpretation of Russian grammar books.) I'll ask about it after posting this.
All speculations aside, allow me to move on to my third and final bullet of knowledge on this topic:
Note how the stress from genitive singular to nominative plural changes, which is what KCd is referring to.