EIS and smartkey go hand in hand-no smartkey, no EIS. The EIS is the module a smartkey is inserted in to.
You are confusing the EIS and smartkey system with DAS. DAS is Driver Authorization, which is any system MB uses to make the engine non-operable if an incorrect key is used. They used several systems. I have info in my library at work which gives the different systems used and a brief description of how they operate. If there is an interest I can transribe some of this info on this thread.
You are correct in your reasoning about the reason a key for a DAS equipped car needs to be ordered via the MB key facility.
I also believe you are correct in assuming you have a bad key, this is not shall we say "uncommon". If the system always works with one key and never works with another, I don't see a need to do any diagnosis, just order a key.