There are plenty of reasons NOT to use SS fasteners on SS code vessels and code piping: cost, lower stress values, risk of galling and risk of Cl stress cracking. We almost never do- our standard for flange fasteners is B7/2H, zinc coated for < 400 F and black oxide finish for 400-800 F. Some customers want the Zn replaced with a fluoropolymer coating (i.e. Xylan).
There are a few reasons to consider SS fasteners:
1) External corrosion conditions, where you're worried about the CS fasteners being eaten either directly or as a result of galvanic corrosion.
2) Concerns about contamination of the stainless steel surface by contact with the carbon steel, leading to premature corrosion of the stainless steel. This is usually a dumb one- not really a concern.
3) Very high temperature operation, where the temperature limits of the CS fasteners are exceeded.
4) Surface cleanliness/cleanability for high purity applications
No inspector should be telling you what needs to be used without a reference.