This would seem to suggest that if boosting a Power+Method combination, only one participant need to know the Power, but every participant need to know the Method. But when talking about the bonus each participant provides to the casting total, we read:
which suggests participants do not need to know the relevant Method. Which is which? Perhaps there is a typo, and participants get to add Characteristic + Power -- so that every participant needs to know the Method, but it's the Power score that gets added? Or perhaps the first part of the text only means that every participant must "pay the costs" that come with the Method (say, if the Method is Purity, every participant must engage in a strenuous activity causing the loss of a fatigue level or a light wound), but this can be done without actually knowing the Method?
That's right. If they were casting a spell, the ceremony lets them all cast it together, so they all take fatigue or spend Confidence to invoke the effect, or chant in Latin and make gestures, whatever it takes to cast it.