Many Alanon(s) and groups go to GREAT effort to keep various religion out of it all.
Higher Power really just means a source higher than ourselves.
If you take the reading literally -- "the group" represents a manifestation (to fancy a word there) of God's Conscious being expressed through the group. In my simple 8 year old mind, I look at my groups as His angels' voices on Earth. Some are good angels, some are "fallen" but at any rate it becomes a Higher Power for us (folks who do Alanon, and have greatly benefited) for us to get good advice and direction.
My too quick view -- quit trying to find something wrong, and get to work.