SJX,
I may have misread your question but maybe I just misunderstood myself (sic) !
I thought Don had written the answer already.
For most applications, screws maintain the integrity of the bond by compression forces and resilience to deformation upon release of those forces (unscrewing). Thus, carbon steel is appropriate, with the added bonus of being easier to machine. later, hardening processes and polishing are applied e.g. old fashioned annealing or chrome finishing. Heat blueing of the screws is another technique.
For the UFO Tourbilllon, the screws are external and need to be decorative. Don chose 316L that is harder to machine but raionalised by no further finishing (read that as hardening) process. Maybe Young's Modulus of 316L steel alloy may not be as appropriate as that of carbon steel for fastening duty but they sure are pretty screws
Maybe the forces on the lugs and exterior case are not too onerous.
Let's see what Don's other reasons are to choose 316L; other than the ones he wrote. I am not a materials scientist per se.
Regards,
MTF
(small print: but I have tiny/small/inconsequential past experience in medical device R&D and implantable alloys)