They seem fairly orthogonal to me. I guess you could frame the connection like this, though: A teacher acclimated to a group can provide more customized instruction; a slightly older instructing student that is cognitively closer to a learning student can provide more customized instruction.
In general I think they provide different functions, though: stability of environment from the looping teacher, and diversity of information sources/instructors from the other student age groups.
Yes, I think when I've heard about it in the past the different student age groups together were most frequently brought up as the primary cause of benefit.
Where I was wondering if there might be a connection is that a multi-grade classroom also (particularly in small schools) means that a student probably will have the same teacher for multiple years (2-4, in most of the cases I've heard of). I realize that's much less extreme than some of the cases mentioned in the article, but it may still be a secondary source of benefit.
In general I think they provide different functions, though: stability of environment from the looping teacher, and diversity of information sources/instructors from the other student age groups.