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The ROM is basically acting as an FPGA.No, it doesn't; neither from a practical, nor from a theoretical point of view. Theoretically, ROMs are equivalent to the class of pure, total, mathematical functions (i.e., each input value maps to exactly one output value), while FPGAs are equivalent to the class of deterministic finite automata, because they contain internal state.
> After all, an FPGA is just a load of units of small ROM areas, with the inputs and outputs linked to each other.
You're forgetting the memory elements – they're crucial to the functionality of FPGAs.
