Yes, the other pics are of umbellatum. I always thought the Star of Bethlehem referred to the O umbellatum and was associated with that particular variety's propensity to spread like wild fire in friendly habitats, Where this association originated I've no idea.
However, in retrospect I see the merit of your interpretation which is supported in the introduction description in some catalogs'
(O. nutans also has a nickname 'Silver Bells').