Valid points, but not _the_ point. There is a big difference between allowing and supporting something.
OO languages _support_ hidden inputs and outputs as well as programming by mutation. They _allow_ programming in a functional style, but you will have to be inventive for it.
FP languages _support_ immutable values, referential transparency and all that. They _allow_ programming by mutation and hidden inputs and outputs, but you will have to be (sometimes very) inventive for it.
OO languages _support_ hidden inputs and outputs as well as programming by mutation. They _allow_ programming in a functional style, but you will have to be inventive for it.
FP languages _support_ immutable values, referential transparency and all that. They _allow_ programming by mutation and hidden inputs and outputs, but you will have to be (sometimes very) inventive for it.