We have some BX runs laid out in a "star" (or spoke-and-hub)
configuration in our basement.

The electrician suggested replacing the old BX with Romex since he
said that the BX relies on the cladding for grounding which can rust
leaving the circuits ungrounded.

Is this a real concern with BX?
Is Romex better than old BX or does the metal cladding give you a
better quality cable?