I have taken 3 photography related courses that all have private groups on FB. I don't use FB in any other capacity but the value of those groups is probably among the highest ROIs on the internet for me (hobby wise at least).

Is the Facebook algorithm, social graph, or anything else that is unique to Facebook coming into play in those private groups?

Yes-ish. Not that facebook is providing anything from their side but the adoption rate of the non-technical participants is sky-high. much higher than what i have seen with private forums. I can only speculate but my guess is that all the participants are already actively using facebook and hence don't have any reasons not to join and use the private groups. Notifications are dealt with quickly because of the already implemented workflow from their side.