But there are other ways you can all find the same key. In the shapenote tradition there would be a designated keyer, who would just have to give the tonic and most folks would find their notes right from there (even, maybe especially, folks who don't know the word "tonic"). Similarly, with people who are used to singing with each other, there are individuals who will come forward and begin strong and clear and the rest of the folks will know to take their lead from that person. If there are several people who trade off this role, they will determine on the fly who will take this role for a particular song, sometimes with nothing more than an exchanged eye movement although sometimes with an explicit comment. In fact, you cannot sing a song as a group without there being somebody who will perform this role, as you discover when somebody who doesn't themselves lead songs asks or in some cases demands that "we" sing something in particular without there being anybody able or willing to do this for that song.
In some ways I am simply talking about who will lead a particular song. And what I'm saying is that even in the most seemingly group-communal singing somebody has to lead the song, even when some of the people there aren't aware that this is happening.
Thus comes the concept of the alpha musician.
In Morris dance, many teams encourage all of their musicians to play for the dances (although my team generally does not, except for our version of Waltzing Matilda). At Morris Ales and any other situation where there are massed dances, you also have many musicians playing together. It is from these Morris musicians that I learned the term "alpha musician" for what I think are obvious reasons. In this case it is not a question of key, but of tempo and rhythm and expression. It can be entertaining at times when various musicians vie for the role, since this is done on the fly as the dance begins.
My point here is that you don't need an organ to keep a congregation in tune, you just need a cultural understanding of alpha musician.