I love such generalized titles. My mathematically modified brain automatically searches for an example when you cannot copy something, then the whole statement is not true. My dog agrees, he cannot be copied over the network :)
In any case, I don't think it follows that an infinite amount of information is necessary to describe e.g. a dog to the extent to which it could be transferred and there being no functional difference to the copy, even though the exact state is not represented.