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We are talking about Galanthus (same to other amaryllids). That other forms of propagation are possible in other families does not prove otherwise.
My experience has been the same as Hagen's and Maggi's, with bulbils forming on pieces of bulb scale (such as bulb tops. bulb top rings, and even small fragments of bulb scale) which I was sure were completely severed from the basal plate and lacking any fragments of basal plate tissue.