Okay, so I went to look for sources to refute this and I found that both my definition and yours are sometimes used so it can mean either.
https://www.theringer.com/mlb/2019/1/23/18193861/multiposition-players-flexibility-jed-lowrie-dj-lemahieu
^ clearly implies that productivity of the player is an important component.
But I've seen other people include the number/breadth of positions (e.g. both infield and outfield) as a requirement.