There's an aspect of this which I haven't yet mentioned, which is the following:

We can imagine different strains of functionalism. The weakest would just be: "A person's mental state supervenes on their (multiply realizable) 'functional state'." This leaves the nature of the relation between functional state and mental state utterly mysterious, and thereby leaves the 'hard problem' looking as 'hard' as it ever did.

But I think a 'thoroughgoing functionalist' wants to go further, and say that a person's mental state is somehow constituted by (or reduces to) the functional state of their brain. It's not a trivial project to flesh out this idea - not simply to clarify what it means, but to begin to sketch out the functional properties that constitute consciousness - but it's one that various thinkers (like Minsky and Dennett) have actually taken up.

And if one ends up hypothesising that what's important for whether a system is 'conscious' is (say) whether it represents information a certain way, has a certain kind of 'higher-order' access to its own state, or whatever - functional properties which can be scaled up and down in scope and complexity without any obvious 'thresholds' being encountered that might correspond to the appearance of consciousness - then one has grounds for saying that there isn't always a 'fact of the matter' as to whether a being is conscious.