Don't worry I wont argue. As for all Balanophyllia species being only a solitary polyp species, I respect your coral biologist's opinion.
Taken from attached link:
Some genera (i.e.,
Endopachys, Eguchipsammia, Balanophyllia) are known to asexually bud smaller coralla from their edges, the parent corallum continuing to increase in size, and one genus (
Notophyllia) asexually propagates by transverse division.
http://tolweb.org/Dendrophylliidae/19165
Mike