Not quite true. You most certainly can hold a CFII without either MEI or CFI. The three instructor ratings are each standalone ratings.
BTW, I hold MEI without the other two. I've also held Oz equivalents to the FAA's instructor rating trio. I'll end up doing the other two at some point but it worked out easier for me to do the MEI first. Lots of multi time or multi instructing time & no experience with the FAA's unique PPL & CPL manoeuvres.