FCC (flat conductor cable) is allowed ONLY in commercial occupancies and ONLY under carpet squares!
The logic is that if there's a problem (meaning a fire), it'll be more apparent in an office setting, and people will be awake and able to evacuate faster.
As for the carpet square thing--I'm guessing that it's because carpet squares are not stretched during installation, like wall-to-wall carpet on a roll. Even though FCC glues down pretty well to cement slab, it could still be damaged by movement of carpet over it.
So, get out the rotp hammer and set it to "chip"...do the job right, do it safe!