That was a GNU documentation problem, never applicable to non-GNU versions of cpio, and not even applicable to the current GNU manual page, which has no mention of info and definitely exists. It also post-dates by years the period where tar and cpio were in competition, which was (roughly) the early 1980s. (The POSIX standard pax aimed at resolving the conflict was in the 1003.1b draft in 1991.) It thus is an entirely fallacious explanation for what happened in the "archiver wars".
* https://news.ycombinator.com/item?id=18978064
* https://netbsd.gw.com/cgi-bin/man-cgi?cpio
And the fact that it’s manpage was missing, only saying “use info instead” did not help its usability at all.