It seems to me that, since three notes are required to spell out a chord, that would be the reason for the ambiguity. Lets take two notes E - G.
I would argue this is ambiguous because by itself it probably would make me hear an e minor harmony if it was spelled out low E high G (somewhere). Turn that around and maybe not.
However, C - E - G would be a C chord. E - G - B would sound like e minor. A - E - G would probably make me think of A7.
I would say that two notes can establish a harmonic progression just fine, just listen to any beginner Bach transcription for classical guitar and you can hear it. However you could easily disrupt that by adding in a third note (Easy Jazz Bach transcriptions for Classical guitar :) ). That third note would have the effect, I believe, in solidifying a harmonic progression that was otherwise ambiguous.
I think that above those three notes, it would be much more difficult to add in notes and actually create the impression of altering the harmonic progression, instead I think it would just end up being colored with extended harmonies.