Do you have any references for that? HCI has been in use since the late 70s (I believe it originated at Xerox PARC, since the earliest literature I can find using it is from there), and is now the de-facto standard term for all major conferences/publications. On the other hand, searching "MMI" on the ACM digital library only returns it as an acronym for various more-or-less related things.
Maybe MMI is a mistranslation from other languages? This Danish site [1] uses it, and I know the used French term is "Interaction Homme Machine", which I can easily imagine being translated to Man-Machine Interaction
It's mentioned here for instance http://en.wikipedia.org/wiki/User_interface. I always got the impression it was a term emerging from the military in the 1940s-50s, when they began to study the ergonomics of cockpits, flight control systems, etc.
Maybe MMI is a mistranslation from other languages? This Danish site [1] uses it, and I know the used French term is "Interaction Homme Machine", which I can easily imagine being translated to Man-Machine Interaction
[1]: http://www.eit.ihk-edu.dk/subjects/mmi/intro.php#0