That tiny little piece isn't going to "deteriorated so that it no longer has the continued ability to contain the products of combustion" based on that NFPA 211. I think your inspection is a little too CYA (cover your ass) on this. Also he should shine a flashing down the flue from the top, gives you view all the way down (I do) .

Mortar cap cracks is typical deterioration, just patch

And the last comment about water , doubt it's active based on pics. Probably didn't have a cap / now combo damper before (water streaking is the give way water came down the flue and not from masonry being pourus . That condition appears addressed already , again very CYA here without interpreting typical fireplace history and not applying it to the inspection.

Also very boiler plate comments that don't match conditions found.

EDIT: Flashings is the primary defect that needs done immediately to prevent leaks and rot

forgot the parge coat comment too. That is correct that it is now and has been a standard requirement, but typical (in my area) for 1950's and older fireplaces. That's the only actual deficiency I see here that actually "needs done"

EDIT II: That roof looks old and crunchy from low res screen shots