I have been using PBL for two decades now. Two things struck me in the goups randomly assigned to work together. I wrote about this extensively in the endnotes section in my book on TE Education since it is something of a hobby horse of mine. The process of using this teaching strategy, even in large groups, is explained fully ther
The group might be dysfunctional for various reasons but usually the two reasons I gave above in the question predominate though I tried to minmise them by randomly assigning group leaders for each group.
I also encountered both problems mentione above during my elearning course, and frankly found the ostracising one much more disturbing personally.
I never liked giving group assignments as an assessment strategy; the PBL presentations were a simple teaching strategy to engage students with learning and further reading as required at HE level.
Once I was constrained by student demands to give them the option of doing an assignment in pairs. If done in pairs both students had to write a small reflection on the whole process. Reading the reflections, everything was as smooth as silk, which made me sceptical of course.
Come a year later I learnt how the assignment was done by one person while the other did the assignment of the other study unit in a couple of instances; so much for the reflective account..
With regards to group assignments allocated by other academics, I had heard too much hoary incidents by students confiding me, to even remotely consider it, hence my duo students effort.