That sounds weird. Did SSH originally have file-copying capabilities? As I recall, the ssh command was written to be command-line compatible with rsh, not telnet, since rsh (and its companion rlogin) was what people were using at the time to log in over the network between local systems. The manual page for SSH still states this explicitly: “It is intended to replace rlogin and rsh […]”, and SSH from the start had (and still has) an rlogin replacement, "slogin". (Telnet was at the time only used for accessing remote, i.e. not-on-site, services, which did not necessarily imply shell access.) Anyway, the rsh and rlogin protocols use port 513 and 514, but no nearby ports seems to be unallocated. The story seems to be missing some details, or possibly be made up after the fact in lieu of a bad memory.
It seemed reasonable to me at the time to give port 22 to a better replacement for, and a spiritual successor to, Telnet, but the story seems odd for not mentioning rsh or rlogin at all.