Okay, I see what you are saying. Regarding this, then:
The basis for authority—moral or otherwise—is a human ability to recognize expertise without at the same time directly recognizing the truths that the expert or authority espouses. I can know that Stephen Hawking has scientific expertise without knowing that the universe began from a singularity. In particular I can know that Hawking has significantly more scientific expertise than I do, and that his opinions are therefore more weighty than my own.
The interesting thing is that Anscombe’s quip that Foot focuses on is arguably centrally related to moral authorities: