I did a little searching in the code, and while some of it is a bit conflicting, I can see where your inspector is making the argument that MC cable is required.
First of all, I'm going to argue that a "Residential Smoke Detector" and a "Fire Alarm System" are the same thing.
[UPDATE: Based on the definision of a "Smoke Detector" as supplied by the IFC, I no longer make this argument. The rest of this post is now irrelevant, other than to indicate AFCI protection is required for smoke detectors].
The reason is because R313.1 of 2006 IRC says that a smoke alarm must be installed per NFPA 72, and 760.1 of 2008 NEC says that a "Fire Alarm System" must be installed per NFPA 72. Additionally, the NEC makes no reference to "smoke alarm" (I did a word search, and you won't find those words in the NEC), and 760.1 FPN No. 1 of 2008 NEC states that "Fire alarm systems include fire detection and alarm notification...", which sounds like a smoke detector to me. So unless there is something that NFPA 72 says otherwise, I think an AHJ can claim a "Residential Smoke Detector" is a sub-set of a "Fire Alarm System".
Now here's where the wording gets a bit aquard, but I think it's where the AHJ gets the requirement for MC...
760.41(B) and 760.121(B) specify that a fire alarm system must be powered from its own branch circuit, and that circuit shall not be protected by AFCI or GFCI. However, 210.12(B)Ex.2 (poorly worded) seems to say AFCI isn't required for a fire alarm system IF the power source is installed in RMC, IMC, EMT, or steel armored cable.
In general it seems that 210.12(B) is saying AFCI protection isn't required IF the cable is protected by MC or conduit (i.g. if you run conduit from the circuit breaker to the 1st outlet, you can place an AFCI in the outlet to protect the circuit rather than an AFCI breaker). However, 760 is basically saying you can't use an AFCI... therefore taken together, since the smoke detectors can't be protected by AFCI, then the wiring must be protected by MC or conduit.