Thank you Adrian.It seems the code is allowing only who has Superuser/Replication role directly.Is there any possibility in future releases they allow both case A & B Users able to use pg_basebackup.
It does not seem wise to introduce inheritance of such powerful capabilities when for many years now we have not done so. It seems like reality could be better documented but the present behavior should stay. I also find the original choice to be quite sane regardless.
David J.