I'm with you - whenever a non-demoninational event goes down, or when someone says "take the higher power of your choice, could be Gandalf, it doesn't matter!" I can't help roll my eyes. It's an ignorant thing to say. Assuming a religion is "invalid" or not a "religion" if it doesn't have a godhead at all. Many don't, named or otherwise. "Higher Power." And lord forbid your chosen godhead is someone else's religion fallman. When I was growing up in SC and we'd do these school classroom prayers (public school, unconstitutional, but who's keeping score?), me being a cringy little 13 year old atheist would say shit like "hail satan" and raise ire of pretty much the entire school. So no, they don't really mean "your higher power of choice," they mean "your given godhead that I can convince myself is actually mine just under a different name."