The wording of this Section has been slightly changed, but the intent is still the same as it was in the '96 NEC. It is exactly as Don stated above.
M/C cable could only be acceptable if the armor was an approved grounding path. I've seen an M/C with a continuous corrugated, not interlocked, armor. Not sure how it was rated or who made it. To my knowledge there's no manufacturer that makes an M/C with an interlocked armor approved as a grounding path.
A/C cable, though is approved.
It sounds like you better break out the EMT bender, as flex isn't acceptable as a grounding path either.(LA used to accept square cut Al flex years ago, but doesn't any longer)

You've got us CA kids wondering to which County you are referring. Please don't keep us guessing.